# Introductory Statistics

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### Problem 1

Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for
a. independent group means, population standard deviations, and/or variances known
b. independent group means, population standard deviations, and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
It is believed that 70% of males pass their drivers test in the first attempt, while 65% of females pass the test in the first attempt. Of interest is whether the proportions are in fact equal. Robin C.

### Problem 2

Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for
a. independent group means, population standard deviations, and/or variances known
b. independent group means, population standard deviations, and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
A new laundry detergent is tested on consumers. Of interest is the proportion of consumers who prefer the new brand over the leading competitor. A study is done to test this. Robin C.

### Problem 3

Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for
a. independent group means, population standard deviations, and/or variances known
b. independent group means, population standard deviations, and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted. Robin C.

### Problem 4

Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for
a. independent group means, population standard deviations, and/or variances known
b. independent group means, population standard deviations, and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion

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### Problem 95

A group of transfer bound students wondered if they will spend the same mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of 54 students at their community college and 66 students at their local four-year university. The sample means were $947 and$1,011, respectively. The population standard deviations are known to be $254 and$87, respectively. Conduct a hypothesis test to determine if the means are statistically the same.

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### Problem 96

Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 31 mpg with a standard deviation of seven mpg. Thirty-one non-hybrid sedans get a mean of 22 mpg with a standard deviation of four mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test to evaluate the manufacturers claim.

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### Problem 97

A baseball fan wanted to know if there is a difference between the number of games played in a World Series when the American League won the series versus when the National League won the series. From 1922 to 2012, the population standard deviation of games won by the American League was 1.14, and the population standard deviation of games won by the National League was 1.11. Of 19 randomly selected World Series games won by the American League, the mean number of games won was 5.76. The mean number of 17 randomly selected games won by the National League was 5.42. Conduct a hypothesis test.

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### Problem 98

One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement “I’m pleased with the way we divide the responsibilities for childcare.” The ratings went from one (strongly agree) to five (strongly disagree). Table 10.26 contains ten of the paired responses for husbands and wives. Conduct a hypothesis test to see if the mean difference in the husband’s versus the wife’s satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife).
$$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Wife's Score } & {2} & {2} & {3} & {3} & {4} & {2} & {1} & {1} & {2} \\ \hline \text { Husband's Score } & {2} & {2} & {1} & {3} & {2} & {1} & {1} & {1} & {2} \\ \hline\end{array}$$

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### Problem 99

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them.

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Harsh G.

### Problem 100

We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the same for the whites and the blacks races in the United States. We randomly pick one year, 1992, to compare the races. The number of suicides estimated in the United States in 1992 for white females is 4,930. Five hundred eighty were aged 15 to 24. The estimate for black females is 330. Forty were aged 15 to 24. We will let female suicide victims be our population.

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Harsh G.

### Problem 101

Elizabeth Mjelde, an art history professor, was interested in whether the value from the Golden Ratio formula, $$\left(\frac{\text { larger }+\text { smaller dimension }}{\text { larger dimension }}\right)$$
was the same in the Whitney Exhibit for works from 1900 to 1919 as for works from 1920
to 1942. Thirty-seven early works were sampled, averaging 1.74 with a standard deviation of 0.11. Sixty-five of the later works were sampled, averaging 1.746 with a standard deviation of 0.1064. Do you think that there is a significant difference in the Golden Ratio calculation?

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Harsh G.

### Problem 102

A recent year was randomly picked from 1985 to the present. In that year, there were 2,051 Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is basically the same or different?

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Harsh G.

### Problem 103

Use the following information to answer the next three exercises. Neuroinvasive West Nile virus is a severe disease that affects a person’s nervous system . It is spread by the Culex species of mosquito. In the United States in 2010 there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1,021 reported cases and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1% level of significance, conduct an appropriate hypothesis test.
• “2011” subscript: 2011 group.
• “2010” subscript: 2010 group
This is:
a. a test of two proportions
b. a test of two independent means
c. a test of a single mean
d. a test of matched pairs.

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Harsh G.

### Problem 104

Use the following information to answer the next three exercises. Neuroinvasive West Nile virus is a severe disease that affects a person’s nervous system . It is spread by the Culex species of mosquito. In the United States in 2010 there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1,021 reported cases and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1% level of significance, conduct an appropriate hypothesis test.
• “2011” subscript: 2011 group.
• “2010” subscript: 2010 group
An appropriate null hypothesis is:
a. $p 2011 \leq p 2010$
b. $p 2011 \leq p 2010$
C. $\mu 2011 \leq \mu 2010$
d. $p_{2011}>p_{2010}$

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Harsh G.

### Problem 105

Use the following information to answer the next three exercises. Neuroinvasive West Nile virus is a severe disease that affects a person’s nervous system . It is spread by the Culex species of mosquito. In the United States in 2010 there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1,021 reported cases and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1% level of significance, conduct an appropriate hypothesis test.
• “2011” subscript: 2011 group.
• “2010” subscript: 2010 group
The p-value is 0.0022. At a 1% level of significance, the appropriate conclusion is
a. There is sufficient evidence to conclude that the proportion of people in the United States in 2011 who contracted neuroinvasive West Nile disease is less than the proportion of people in the United States in 2010 who contracted neuroinvasive West Nile disease.
b. There is insufficient evidence to conclude that the proportion of people in the United States in 2011 who
contracted neuroinvasive West Nile disease is more than the proportion of people in the United States in 2010
who contracted neuroinvasive West Nile disease.
c. There is insufficient evidence to conclude that the proportion of people in the United States in 2011 who
contracted neuroinvasive West Nile disease is less than the proportion of people in the United States in 2010 who contracted neuroinvasive West Nile disease.
d. There is sufficient evidence to conclude that the proportion of people in the United States in 2011 who contracted neuroinvasive West Nile disease is more than the proportion of people in the United States in 2010 who contracted neuroinvasive West Nile disease

HG
Harsh G.

### Problem 106

Researchers conducted a study to find out if there is a difference in the use of eReaders by different age groups. Randomly selected participants were divided into two age groups. In the 16- to 29-year-old group, 7% of the 628 surveyed use eReaders, while 11% of the 2,309 participants 30 years old and older use eReaders.

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Harsh G.

### Problem 107

Adults aged 18 years old and older were randomly selected for a survey on obesity. Adults are considered obese if their body mass index (BMI) is at least 30. The researchers wanted to determine if the proportion of women who are obese in the south is less than the proportion of southern men who are obese. The results are shown in Table 10.27. Test at the 1% level of significance.
$$\begin{array}{|c|c|}\hline &{ \text{ Number who are obese} } & {\text { Sample size }} \\ \hline \text { Men } & {42,769} & {155,525} \\ \hline \text { women } & {67,169} & {248,775} \\ \hline\end{array}$$

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Harsh G.

### Problem 108

Two computer users were discussing tablet computers. A higher proportion of people ages 16 to 29 use tablets than the proportion of people age 30 and older. Table 10.28 details the number of tablet owners for each age group. Test at the 1% level of significance.
$$\begin{array}{|c|c|c|}\hline & {16-29 \text { year olds }} & {30 \text { years old and older }} \\ \hline \text { Own a Tablet } & {69} & {231} \\ \hline\end{array}$$
$$\begin{array}{|c|c|c|c|}\hline & {16-29 \text { year olds }} & {30 \text { years old and older }} \\ \hline \text { Sample Size } & {628} & {2,309} \\ \hline\end{array}$$

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Harsh G.

### Problem 109

A group of friends debated whether more men use smartphones than women. They consulted a research study of smartphone use among adults. The results of the survey indicate that of the 973 men randomly sampled, 379 use smartphones. For women, 404 of the 1,304 who were randomly sampled use smartphones. Test at the 5% level of significance.

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Harsh G.

### Problem 110

While her husband spent 21?2 hours picking out new speakers, a statistician decided to determine whether the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment. The population was Saturday afternoon shoppers. Out of 67 men, 24 said they enjoyed the activity. Eight of the 24 women surveyed claimed to enjoy the activity. Interpret the results of the survey.

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Harsh G.

### Problem 111

We are interested in whether children’s educational computer software costs less, on average, than children’s entertainment software. Thirty-six educational software titles were randomly picked from a catalog. The mean cost was $31.14 with a standard deviation of$4.69. Thirty-five entertainment software titles were randomly picked from the same catalog. The mean cost was $33.86 with a standard deviation of$10.87. Decide whether children’s educational software costs less, on average, than children’s entertainment software.

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Harsh G.

### Problem 112

Joan Nguyen recently claimed that the proportion of college-age males with at least one pierced ear is as high as the proportion of college-age females. She conducted a survey in her classes. Out of 107 males, 20 had at least one pierced ear. Out of 92 females, 47 had at least one pierced ear. Do you believe t at the proportion of males has reached the proportion of females?

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Harsh G.

### Problem 113

Use the data sets found in Appendix C to answer this exercise. Is the proportion of race laps Terri completes slower than 130 seconds less than the proportion of practice laps she completes slower than 135 seconds?

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### Problem 114

"To Breakfast or Not to Breakfast?" by Richard Ayore
In the American society, birthdays are one of those days that everyone looks forward to. People of different ages and peer groups gather to mark the 18th, 20th, ..., birthdays. During this time, one looks back to see what he or she has achieved for the past year and also focuses ahead for more to come.If, by any chance, I am invited to one of these parties, my experience is always different. Instead of dancing around with my friends while the music is booming, I get carried away by memories of my family back home in Kenya. I remember the good times I had with my brothers and sister while we did our daily routine. Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one day arguing with my brother as to why he always remained behind just to join us an hour later. In his defense, he said that he preferred waiting for breakfast before he came to weed. He said, “This is why I always work more hours than you guys!” And so, to prove him wrong or right, we decided to give it a try. One day we went to work as usual without breakfast, and recorded the time we could work before getting tired and stopping. On the next day, we all ate breakfast before going to work. We recorded how long we worked again before getting tired and stopping. Of interest was our mean increase in work time. Though not sure, my brother insisted that it was more than two hours. Using the data in Table 10.29, solve our problem.
table cannot copy

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Harsh G.

### Problem 115

Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. The data are recorded in Table 10.30. Do you think that their cholesterol levels were significantly lowered?
table cannot copy

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Harsh G.

### Problem 116

Use the following information to answer the next two exercises. A new AIDS prevention drug was tried on a group of 224 HIV positive patients. Forty-five patients developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after four years. We want to test whether the method of treatment reduces the proportion of patients that develop AIDS after four years or if the proportions of the treated group and the untreated group stay the same. Let the subscript t = treated patient and ut = untreated patient.
The appropriate hypotheses are:
a. $H_{0} : p_{t}<p u t$ and $H a : p_{t} \geq p_{u t}$
b. $H_{0} : p_{t} \leq p_{u t}$ and $H_{a} : p_{t}>p_{u t}$
c. $H_{0} : p_{t}=p_{u t}$ and $H_{a} : p_{t} \neq p_{u t}$
d. $H_{0} : p_{t}=p u t$ and $H a : p_{t}<p_{u t}$

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Harsh G.

### Problem 117

Use the following information to answer the next two exercises. A new AIDS prevention drug was tried on a group of 224 HIV positive patients. Forty-five patients developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after four years. We want to test whether the method of treatment reduces the proportion of patients that develop AIDS after four years or if the proportions of the treated group and the untreated group stay the same. Let the subscript t = treated patient and ut = untreated patient.
If the $p$ -value is 0.0062 what is the conclusion (use $\alpha=0.05 ) ?$
a. The method has no effect.
b. There is sufficient evidence to conclude that the method reduces the proportion of HIV positive patients who develop AIDS after four years.
c. There is sufficient evidence to conclude that the method increases the proportion of HIV positive patients who develop AIDS after four years.
d. There is insufficient evidence to conclude that the method reduces the proportion of HIV positive patients who develop AIDS after four years.

HG
Harsh G.

### Problem 118

Use the following information to answer the next two exercises. An experiment is conducted to show that blood pressure can be consciously reduced in people trained in a “biofeedback exercise program.” Six subjects were randomly selected and blood pressure measurements were recorded before and after the training. The difference between blood pressures was calculated (after - before) producing the following results: $\overline{x}_{d}=-10.2 \mathrm{sd}=8.4$ Using the data, test the hypothesis that the blood pressure has decreased after the training.
The distribution for the test is:
a. $t 5$
b. $t_{6}$
c. $N(-10.2,8.4)$
d. $\mathrm{N}\left(-10.2, \frac{8.4}{\sqrt{6}}\right)$

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Harsh G.

### Problem 119

Use the following information to answer the next two exercises. An experiment is conducted to show that blood pressure can be consciously reduced in people trained in a “biofeedback exercise program.” Six subjects were randomly selected and blood pressure measurements were recorded before and after the training. The difference between blood pressures was calculated (after - before) producing the following results: $\overline{x}_{d}=-10.2 \mathrm{sd}=8.4$ Using the data, test the hypothesis that the blood pressure has decreased after the training.
If $\alpha=0.05,$ the $p$ -value and the conclusion are
a. 0.0014; There is sufficient evidence to conclude that the blood pressure decreased after the training.
b. 0.0014; There is sufficient evidence to conclude that the blood pressure increased after the training.
c. 0.0155; There is sufficient evidence to conclude that the blood pressure decreased after the training.
d. 0.0155; There is sufficient evidence to conclude that the blood pressure increased after the training.

HG
Harsh G.

### Problem 120

A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She
takes four new students. She records their 18-hole scores before learning the technique and then after having taken her class.
She conducts a hypothesis test. The data are as follows.
$$\begin{array}{|c|c|c|c|}\hline & {\text { Player } 1} & {\text { Player } 2} & {\text { Player } 3} & {\text { Player } 4} \\ \hline \text { Mean score before class } & {78} & {78} & {93} & {87} \\ \hline \text { Mean score after class } & {80} & {80} & {86} & {86} \\ \hline\end{array}$$
The correct decision is:
a. Reject $H_{0}$ .
b. Do not reject the Ho.

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Harsh G.

### Problem 121

A local cancer support group believes that the estimate for new female breast cancer cases in the south is higher in
2013 than in 2012. The group compared the estimates of new female breast cancer cases by southern state in 2012 and in
2013. The results are in Table 10.32.
$$\begin{array}{|l|l|l|l|}\hline \text { Southern States } & {2012} & {2013} \\ \hline \text { Alabama } & {3,450} & {3,720} \\ \hline \text { Arkansas } & {2,150} & {2,280} \\ \hline \text { Florida } & {15,540} & {1,310} \\ \hline \text { Georgia } & {6,970} & {7,310} \\ \hline \text { Keorgia } & {3,160} & {3,080} \\ \hline \text { Morth Carolina } & {7,090} & {7,430} \\ \hline \text { Oklahoma } & {2,630} & {2,690} \\ \hline\end{array}$$
$$\begin{array}{|l|l|l|l|}\hline \text { Southern States } & {2012} & {2013} \\ \hline \text { South Carolina } & {3,570} & {3,580} \\ \hline \text { Tennessee } & {4,680} & {5,070} \\ \hline \text { Texas } & {15,050} & {14,980} \\ \hline \text { Virginia } & {6,190} & {6,280} \\ \hline\end{array}$$

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Harsh G.

### Problem 122

A traveler wanted to know if the prices of hotels are different in the ten cities that he visits the most often. The list
of the cities with the corresponding hotel prices for his two favorite hotel chains is in Table 10.33. Test at the 1% level of
significance.
table cannot copy Danielle F.

### Problem 123

A politician asked his staff to determine whether the underemployment rate in the northeast decreased from 2011 to 2012. The results are in Table 10.34.
table cannot copy

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Harsh G.

### Problem 124

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. The population standard deviations are two pounds and three pounds, respectively. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet.

HG
Harsh G.

### Problem 125

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
A new chocolate bar is taste-tested on consumers. Of interest is whether the proportion of children who like the new chocolate bar is greater than the proportion of adults who like it.

HG
Harsh G.

### Problem 126

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
The mean number of English courses taken in a two–year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from nine males and 16 females.

HG
Harsh G.

### Problem 127

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
A football league reported that the mean number of touchdowns per game was five. A study is done to determine if the mean number of touchdowns has decreased.

HG
Harsh G.

### Problem 128

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
A study is done to determine if students in the California state university system take longer to graduate than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. From years of research, it is known that the population standard deviations are 1.5811 years and one year, respectively.

HG
Harsh G.

### Problem 129

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
According to a YWCA Rape Crisis Center newsletter, 75% of rape victims know their attackers. A verify this.

HG
Harsh G.

### Problem 130

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
According to a recent study, U.S. companies have a mean maternity-leave of six weeks.

HG
Harsh G.

### Problem 131

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
A recent drug survey showed an increase in use of drugs and alcohol among local high school students as compared to the national percent. Suppose that a survey of 100 local youths and 100 national youths is conducted to see if the proportion of drug and alcohol use is higher locally than nationally.

HG
Harsh G.

### Problem 132

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
A new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded. Of interest is the mean increase in SAT scores. The following data are collected: table cannot copy

HG
Harsh G.

### Problem 133

Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.
a. independent group means, population standard deviations and/or variances known
b. independent group means, population standard deviations and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
University of Michigan researchers reported in the Journal of the National Cancer Institute that quitting smoking is especially beneficial for those under age 49. In this American Cancer Society study, the risk (probability) of dying of lung cancer was about the same as for those who had never smoked.

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Harsh G.

### Problem 134

Lesley E. Tan investigated the relationship between left-handedness vs. right-handedness and motor competence in preschool children. Random samples of 41 left-handed preschool children and 41 right-handed preschool children were given several tests of motor skills to determine if there is evidence of a difference between the children based on this experiment. The experiment produced the means and standard deviations shown Table 10.36. Determine the appropriate test and best distribution to use for that test.
$$\begin{array}{|l|l|l|}\hline & {\text { Left-handed }} & {\text { Right-handed }} \\ \hline \text { sample size } & {41} & {41} \\ \hline \text { Sample mean } & {97.5} & {98.1} \\ \hline \text { Sample standard deviation } & {17.5} & {19.2} \\ \hline\end{array}$$

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Harsh G.

### Problem 135

A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takes four (4) new students. She records their 18-hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as Table 10.37.
$$\begin{array}{|c|c|c|c|}\hline & {\text { Player } 1} & {\text { Player } 2} & {\text { Player } 3} & {\text { Player } 4} \\ \hline \text { Mean score before class } & {78} & {78} & {93} & {87} \\ \hline \text { Mean score after class } & {80} & {80} & {86} & {86} \\ \hline\end{array}$$
This is:
a. a test of two independent means.
b. a test of two proportions.
c. a test of a single mean.
d. a test of a single proportion.

HG
Harsh G.