Currently teaching statistics and pre-calculus classes.
Among $21-$ to 25 -year-olds, 29\% say they have driven while under the influence of alcohol. Suppose that three $21-$ to 25 -year-olds are selected at random. Source: U.S. Department of Health and Human Services, reported in USA Today(a) What is the probability that all three have driven while under the influence of alcohol?(b) What is the probability that at least one has not driven while under the influence of alcohol?(c) What is the probability that none of the three has driven while under the influence of alcohol?(d) What is the probability that at least one has driven while under the influence of alcohol?
Describe the distribution of sample means (shape, mean, standard error) for samples of $n=64$ selected from a population with a mean of $\mu=90$ and a standard deviation of $\sigma=32$
A researcher wants to estimate the average distance that students at a large community college live from campus. To find out, she surveys a simple random sample of students from the registrar's database. (a) Will the researcher's sample result be exactly the same as the true population mean? Explain.(b) Which would be more likely to get the researcher's sample result closer to the true population value:an SRS of 100 students or an SRS of 50 students?Explain.
Suppose you want to know the average amount of money spent by the fans attending opening day for the Cleveland Indians baseball season. You get permission from the team's management to conduct a survey at the stadium, but they will not allow you to bother the fans in the club seating or box scats (the most expensive seating). Using a computer, you randomly select 500 seats from the rest of the stadium. During the game, you ask the fans in those seats how much they spent that day. Give a reason why this survey might yield a biased result. Explain the likely direction of the bias.
3 About 77% of young adults think they canachieve the American dream. a) Determine if the following statements are true orfalse, and explain your reasoning.The distribution of the sample proportions of youngAmericans, in random samples of size 20, who think they can achievethe American dream is left skewed.The distribution of the sample proportions of youngAmericans, in random samples of size 40, who think they can achievethe American dream is approximately normal since n ≥30.b) In a random sample of 120 youngAmericans, what is the probability that 85% or more think they canachieve the Americandream? c) Given your answer in part c, should arandom sample of 120 young Americans in which 85% think they canachieve the American dream be considered unusual? Why or whynot?
In a clinical study, 3400 healthy subjects aged 18-49 werevaccinated with a vaccine against a seasonal illness. Over a periodof roughly 28 weeks, 24 of these subjects developed theillness. Complete parts a through e below.a. Find the point estimate of the population proportion thatwere vaccinated with the vaccine but still developed the illness.The point estimate is nothing. (Round to five decimal places asneeded.)b. Find the standard error of this estimate. The standard errorof this estimate is nothing. (Round to five decimal places asneeded.)c. Find the margin of error for a 95% confidence interval. Themargin of error is nothing. (Round to five decimal places asneeded.)d. Construct the 95% confidence interval for the populationproportion. Interpret the interval. The 95% confidence intervalfor the population proportion is (__,__). (Round to five decimalplaces as needed.)Interpret the interval. Choose the correct answer below.A. With 95% confidence, the limits of the confidence intervalcontain the proportion of healthy people aged 18-49 who arevaccinated with the vaccine but still develop the illness.B. The proportion of all people who are vaccinated with thevaccine but still develop the illness falls within the limits ofthe confidence interval 95% of the time.C. With 95% confidence, the limits of the confidence intervalcontain the proportion of healthy people aged 18-49 who arevaccinated with the vaccine who do not develop the illness.D. The proportion of healthy people aged 18-49 who arevaccinated with the vaccine but still develop the illness fallswithin the limits of the confidence interval 95% of the time.e. Is it safe to conclude that fewer than 1% of all the peopleaged 18-49 vaccinated with the vaccine will develop the illness?Explain by using the results from part d.A. No, it should not be concluded, since the lower limit ofthe confidence interval is greater than 0.01.B. Yes, it can be concluded, since the lower limit of theconfidence interval is less than 0.01.C. No, it should not be concluded, since the upper limit ofthe confidence interval is greater than 0.01.D. Yes, it can be concluded, since the upper limit of theconfidence interval is less than 0.01.
You are studying the effects of smoking by pregnant women onrates of asthma in their children. You collect data on the numberof cigarettes smoked per day and whether or not the child developedasthma by the age of two. The data is below: Smoked 1-5 cigarettesper day --- 8.8% developed asthma Smoked 6-10 cigarettes per day--- 9.8% developed asthma Smoked 11-20 cigarettes per day --- 25.1%developed asthma Smoked 21-40 cigarettes per day --- 35.2%developed asthma Smoked 41-60 cigarettes per day --- 38.4%developed asthma In order to study the relationship between thenumber of cigarettes smoked by pregnant women per day and thepercentage of their children developed asthma by the age of twousing statistical knowledge, we convert the above data into thefollowing format and see if we can obtain an adequate fit usinglinear regression.Average number of cigarettes smoked per day3815.530.550.5Percentage of children developed asthma8.8%9.8%25.1%35.2%38.4%What is the value of the correlation coefficient?r = (Round your answer to 4 decimal places.)Assume that the best-fit line of the above data set is a goodmodel for the study. For expectant mothers who smoke 46 cigarettesper day, what is the expected percentage of children who willdevelop asthma by the age of two.percent (Round your answer to 1 decimal place.)
The amount of fuel used by jumbo jets to take off isapproximately normally distributed with a mean of 4000 gallons anda standard deviation of 125 gallons.a. What is the probability that a randomly selected jumbo jetwill need more than 4250 gallons of fuel to take off?b. What is the shape, mean, and standard deviation of thesampling distribution of the mean gallons of fuel to take off of 40randomly selected jumbo jets?c. In a random sample of 40 jumbo jets, what is the probabilitythat the mean number of gallons of fuel needed to take off is lessthan 3950?
The Acme Company manufactures widgets. The distribution ofwidget weights is bell-shaped. The widget weights have a mean of 54ounces and a standard deviation of 4 ounces.Use the Empirical Rule, also known as the 68-95-99.7 Rule. Donot use Tables or Technology to avoid rounding errors.Suggestion: sketch the distribution in order to answer thesequestions.a) 95% of the widget weights lie between and b) What percentage of the widget weights lie between 42 and 62ounces? %c) What percentage of the widget weights lie above 50 ?
Last year, 52% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 40% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners.(a) How many business owners in the survey plan to provide a holiday gift?(b) Suppose the business owners in the sample did as they plan. Compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. Find the value of the test statistic. (Round your answer to two decimal places.) Find the P value.(c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased? What is the smallest level of significance for which you could draw such a conclusion? (Round your answer to four decimal places.)
