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Statistics Learning From Data

Thomas H. Short, Roxy Peck

Chapter 10

Asking and Answering Questions About a Population Proportion - all with Video Answers

Educators

Section 1

Hypotheses and Possible Conclusions

03:29

Problem 1

Explain why the statement $\hat{p}=0.40$ is not a legitimate hypothesis.

Willis James
Willis James
Numerade Educator
02:36

Problem 2

CareerBuilder.com conducted a survey to learn about the proportion of employers who perform background checks when evaluating a candidate for employment ("Majority of Employers Background Check Employees...Here's Why," November $17,$ $2016,$ retrieved November 19,2016 ). Suppose you are interested in determining if the resulting data provide strong evidence in support of the claim that more than two-thirds of employers perform background checks. To answer this question, what null and alternative hypotheses should you test? (Hint: See Example $10.4 .)$

Jorge Villanueva
Jorge Villanueva
Numerade Educator
03:47

Problem 3

The article "Facebook Use and Academic Performance Among College Students," Computers in Human Behavior [2015]:
$265-272$ ) estimated that $70 \%$ of students at a large public university in California who are Facebook users log into their Facebook profiles at least six times a day. Suppose that you plan to select a random sample of 400 students at your college. You will ask each student in the sample if they are a Facebook user and if they log into their Facebook profile at least six times a day. You plan to use the resulting data to decide if there is evidence that the proportion for your college is different from the proportion reported in the article for the college in Califomia. What hypotheses should you test? (Hint: See Example $10.3 .)$

Nick Johnson
Nick Johnson
Numerade Educator
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Problem 4

The article "Poll Finds Most Oppose Return to Draft, Wouldn't Encourage Children to Enlist" (Associated Press, December 18,2005 ) reports that in a random sample of 1000 American adults, 430 answered "yes" to the following question:
"If the military draft were reinstated, would you favor drafting women as well as men?" The data were used to test $H_{0}: p=0.5$ versus $H_{a}: p<0.5,$ and the null hypothesis was rejected. (Hint:
See discussion following Example $10.5 .$ )
a. Based on the result of the hypothesis test, what can you conclude about the proportion of American adults who fayor drafting women if a military draft were reinstated?
b. Is it reasonable to say that the data provide strong support for the alternative hypothesis?
c. Is it reasonable to say that the data provide strong evidence against the null hypothesis?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:01

Problem 5

According to an article in Science Daily ("Sill No Strong Evidence That Adjunct Treatment with HGH in IVF Improves Results," sciencedaily.com, July $4,2016,$ retrieved November 26,2016 ), women who are having difficulty becoming pregnant sometimes use human growth hormone (HGH) in addition to in-vitro fertilization (IVF) to try to have a baby. A large study found that "there was no strong evidence" that the proportion of women who became pregnant while taking HGH along with IVF was greater than the success rate for IVF alone.
a. Is this consistent with testing $H_{0}:$ HGH in addition to IVF increases the chance of getting pregnant versus
$H_{i}: \mathrm{HGH}$ in addition to IVF does not increase the chance of getting pregnant or with testing $H_{0}:$ HGH in addition to IVF does not increase the chance of getting pregnant versus
$H_{i}:$ HGH in addition to IVF increases the chance of getting pregnant Explain.
b. Does the stated conclusion of "no strong evidence" indicate that the null hypothesis was rejected? Explain.

R M
R M
Numerade Educator
00:36

Problem 6

In a hypothesis test, what does it mean to say that the null hypothesis was rejected?

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
03:29

Problem 7

Explain why the statement $\hat{p}>0.50$ is not a legitimate hypothesis.

Willis James
Willis James
Numerade Educator
01:20

Problem 8

USA TODAY (March 4, 2010) described a survey of 1000 women age 22 to 35 who work full time. Each woman who participated in the survey was asked if she would be willing to give up some personal time in order to make more money. To determine if the resulting data provided convincing evidence that the majority of women age 22 to 35 who work full time would be willing to give up some personal time for more money, what hypotheses should you test?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
03:47

Problem 9

The article "Facebook Use and Academic Performance Among College Students" (Computers in Human Behavior $[2015]: 265-272)$ estimated that $87 \%$ percent of students at a large public university in California who are Facebook users update their status at least two times a day. Suppose that you plan to select a random sample of 400 students at your college. You will ask each student in the sample if they are a Facebook user and if they update their status at least two times a day. You plan to use the resulting data to decide if there is evidence that the proportion for your college is different from the proportion reported in the article for the college in California. What hypotheses should you test?

Nick Johnson
Nick Johnson
Numerade Educator
02:00

Problem 10

The article "Public Acceptability in the UK and the USA of Nudging to Reduce Obesity: The Example of Reducing Sugar-Sweetened Beverages" (PLOS One, June 8,2016 ) describes a survey in which each person in a representative sample of 1082 adult Americans was asked about whether they would find different types of interventions acceptable in an effort to reduce consumption of sugary beverages. When asked about a tax on sugary beverages, 459 of the people in the sample said they thought that this would be an acceptable intervention. These data were used to test $H_{0}: p=0.5$ versus $H_{a^{*}}: p<0.5$ and the null hypothesis was rejected.
a. Based on the hypothesis test, what can you conclude about the proportion of adult Americans who think that taxing sugary beverages is an acceptable intervention in an effort to reduce consumption of sugary beverages?
b. Is it reasonable to say that the data provide strong support for the alternative hypothesis?
c. Is it reasonable to say that the data provide strong evidence against the null hypothesis?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
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Problem 11

A press release about a paper that appeared in The Journal of Youth and Adolescence (www.springer.com/ about1springer/media/springertselect?SGWID50-11001-6 $-1433942-0,$ August $26,2013,$ retrieved May 8,2017$)$ was titled "Video Games Do Not Make Vulnerable Teens More Violent." The press release includes the following statement about the study described in the paper: "Study finds no evidence that violent video games increase antisocial behavior in youths with pre-existing psychological conditions." In the context of a hypothesis test with the null hypothesis being that video games do not increase antisocial behavior, explain why the title of the press release is misleading.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
00:36

Problem 12

In a hypothesis test, what does it mean to say that the null hypothesis was not rejected?

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
04:27

Problem 13

Which of the following are legitimate hypotheses?
a. $p=0.65$
b. $\hat{p}=0.90$
c. $p=0.10$
d. $p=0.45$
e. $p>4.30$

Sonam Khatri
Sonam Khatri
Numerade Educator
01:58

Problem 14

Which of the following specify legitimate pairs of null and alternative hypotheses?
a. $H_{0}: p=0.25 \quad H_{i}: p>0.25$
b. $H_{0}: p<0.40 \quad H_{i}: p>0.40$
c. $H_{0}: p=0.40 \quad H: p<0.65$
d. $H_{0}: p \neq 0.50 \quad H_{i}: p=0.50$
e. $H_{\mathrm{n}}: p=0.50 \quad H_{i}: p>0.50$
f. $H_{0}: \hat{p}=0.25 \quad H_{e^{\prime}} \hat{p}>0.25$

Christopher Stanley
Christopher Stanley
Numerade Educator
01:30

Problem 15

A college has decided to introduce the use of plus and minus with letter grades, as long as there is convincing evidence that more than $60 \%$ of the faculty favor the change. A random sample of faculty will be selected, and the resulting data will be used to test the relevant hypotheses. If $p$ represents the proportion of all faculty who favor a change to plus-minus grading, which of the following pairs of hypotheses should be tested?
$$
H_{0^{*}} p=0.6 \text { versus } H_{i}: p<0.6
$$
or
$$
H_{0}: p=0.6 \text { versus } H_{e}: p>0.6
$$
Explain your choice.

Hossam Mohamed
Hossam Mohamed
Numerade Educator
01:31

Problem 16

A television station has been providing live coverage of a sensational criminal trial. The station's program director wants to know if more than half of potential viewers prefer a return to regular daytime programming. A survey of randomly selected viewers is conducted. With $p$ representing the proportion of all viewers who prefer regular daytime programming, what hypotheses should the program director test?

Nick Johnson
Nick Johnson
Numerade Educator