Exam 9: Inferring Population Means

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours. -Choose the statement that describes a situation where a confidence interval and a hypothesis test will yield the same results.

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours. -What is the standard error for the mean finish time of 30 randomly selected participants in the 40-44 age group? Round to the nearest thousandth.

An economist conducted a hypothesis test to test the claim that the average cost of eating a meal away from home decreased from 2009 to 2010. The Average cost of eating a meal away from home in 2009 was $7.15 per person per meal. Assume that All Conditions for testing have been met. He used technology to complete the hypothesis test. Following is his Null and alternative hypothesis and the output from his graphing calculator. :\mu=\ 7.15 :\mu<\ 7.15 T-Test \mu<7.15 t=-1.043281062 p=.1527187422 =6.95 Sx=1.05 n=30 Choose the statement that contains the correct conclusion regarding the hypothesis and the original Claim.

State whether the situation has dependent or State whether the situation has dependent or independent samples. A researcher wants toknow if reaction time is affected by the gender of the driver. He measures the reaction timeof 30 female drivers while they drive a compact car, then he measures the reaction time of 30 male drivers while they drive a compact car.

What is the expected finish time for a male participant in the sample of 30? Will theexpected mean finish time be the same for any sample of 30 males drawn from thepopulation? Explain.

Suppose a consumer product researcher wanted to find out whether a printer ink cartridgelasted longer than the manufacturer's claim that their ink cartridges could print 400 pages.The researcher tested 40 ink cartridges and recorded the number of pages that wereprinted before the ink started to fade. Test the hypothesis that the ink cartridges lasted formore than 400 pages. Following are the summary statistics: $\bar { x } = 415 \text { pages, } s = 30 \text { pages }$ Be sure to report the null and alternative hypothesis, test statistic, p-value, your decisionregarding the null hypothesis, and your conclusion about the original claim. Round allvalues to the nearest thousandth.

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours. -Suppose a consumer product researcher wanted to find out whether a highlighter lasted longer than the manufacturer's claim that their highlighters could write continuously for 14 hours. The Researcher tested 40 highlighters and recorded the number of continuous hours each highlighter Wrote before drying up. Test the hypothesis that the highlighters wrote for more than 14 Continuous hours. Following are the summary statistics: $\bar { x } = 14.5 \text { hours, } s = 1.2 \text { hours }$ Report the test statistic, p-value, your decision regarding the null hypothesis. At the 5% Significance level, state your conclusion about the original claim. Round all values to the nearest Thousandth.

An economist conducted a hypothesis test to test the claim that the average cost of eating a meal at home increased from 2009 to 2010. The average cost of eating a meal at home in 2009 was $5.25 per Person per meal. Assume that all conditions for testing have been met. He used technology to Complete the hypothesis test. Following is his null and alternative hypothesis and the output from His graphing calculator. :\mu=\ 5.25 :\mu>\ 5.25 T-Test \mu>5.25 t=4.644687288 p=3.4015934E-5 =6.31 Sx=1.25 n=30 At the 5% significance level, choose the statement that contains the correct conclusion regarding the Hypothesis and the original claim.

Suppose that the average country song length in America is 4.75 minutes with a standard deviation of 1.10 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 Songs is taken from the population. What is the approximate probability that the average song Length will last more than 5.25 minutes? Round to the nearest thousandth.

Suppose that the average country song length in America is 4.75 minutes with a standard deviation of 1.10 minutes. It is known that song length is not normally distributed. Find the probability that a Single randomly selected song from the population will be less than 4.20 minutes. Round to the Nearest thousandth.

The weights at birth of five randomly chosen baby Orca whales were 425, 454, 380, 405, and 426 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval For the mean weight of all baby Orca whales. Use technology for your calculations. Give the Confidence interval in the form "estimate ± margin of error." Round to the nearest tenth of a pound.

Use the following information to answer the question. Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to the website www.costofwedding.com, the average cost of a wedding in the U.S. in 2009 was $24,066. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of a wedding was $23,224, with a standard deviation of $2,903. On the basis of this, a 95% confidence interval for the mean cost of weddings in the U.S. is $22,296 to $24,152. -Does the confidence interval provide evidence that the mean cost of a wedding has decreased?

Which of the following is not a true statement about the Central Limit Theorem for sample means?

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours. -In this example, the numerical values of 1.62 hours and 0.40 hours are .

A sociologist wants to know whether there is a difference in the mean number of times thatmen and women in the U.S. check their Smartphone during the day. Test the hypothesisthat the mean number of times that men and women in the U.S. check their Smartphoneduring the day is different. Following are the summary statistics: Men Women n=25 n=40 =30 checks per day =35 checks per day s=6 checks per day s=7 checks per day Assume that all conditions for testing have been met. Be sure to report the null andalternative hypothesis, test statistic, p-value, your decision regarding the null hypothesis,and your conclusion about the original claim. Round all values to the nearest thousandth.

Which of the following is not a true statement about the Central Limit Theorem for sample means?

The weights at birth of five randomly chosen baby hippopotamuses were 75, 99, 107, 82, and 63 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby hippopotamuses. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error." Round to the nearest pound.

Use the following information to answer the question. According to the website www.costofwedding.com, the average costof catering a wedding (with an open bar) is $100 per person. Recently, in a random sample of 40 weddings in the U.S. it wasfound that the average catering cost was $110, with a standard deviation of $12. On the basis of this, a 95% confidenceinterval for the mean catering cost for a wedding is $106 to $114. -A popular wedding magazine states in an article on catering costs that "There is a 95%chance that the catering cost of your wedding will be between $106 and $114 per person."Explain what is wrong with this statement and write a better statement that correctlyinterprets the confidence interval.

Use the following information to answer the question. Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to the website www.costofwedding.com, the average cost of a wedding in the U.S. in 2009 was $24,066. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of a wedding was $23,224, with a standard deviation of $2,903. On the basis of this, a 95% confidence interval for the mean cost of weddings in the U.S. is $22,296 to $24,152. -Choose the statement that is the best interpretation of the confidence interval.

Which of the following statements is not true about the t-distribution?