Exam 9: Inferring Population Means

Suppose a consumer product researcher wanted to find out whether a highlighter lasted less 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 less than 14 continuous hours. Following are the summary statistics: x =13.6 hours, s =1.3 hours Report the test statistic, p- value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.

Use the following information to answer the question. According to the website ww.costofwedding.com, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767. -Choose the statement that is the best interpretation of the confidence interval.

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 .

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

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

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. H₀: µ = $7.15 H_a: µ < $7.15 Choose the statement that contains the correct conclusion regarding the hypothesis and the original claim.

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. -Suppose the process of taking random samples of size 30 from the 40- 44 age group is repeated 200 times and a histogram of the 200 sample means is created. Which statement best describes the shape of the histogram?

State whether the situation has dependent or independent samples. A researcher wants to know if reaction time is affected by body type of the vehicle being driven. He measures the reaction time of 40 drivers while they drive a compact car then he measures the reaction time while they drive an SUV.

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

How might the shapes of a population distribution and a sampling distribution look the same? How might they look different?

The productivity of manufacturing plant workers is compared before and after the installation of air conditioning.

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.

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 HYPERLINK "http://www.costofwedding.com/" 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?

Choose the statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean.

A chewing gum manufacturer wants to know whether students score higher on math tests when they are allowed to chew gum during a test. He conducts an experiment with a sample of four randomly selected students and records the test results with gum chewing and without. Test the hypothesis that test scores were higher when students were allowed to chew gum during the test. Following are the test scores for the four participants: Assume that all conditions for testing have been met. Be sure to report the null and alternative 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.

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 the process of taking random samples of size 30 is repeated 200 times and a histogram of the 200 sample means is created. Would the histogram be an approximate display of the population distribution, the distribution of a sample, or the sampling distribution of 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. 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.

The college GPA's of identical twins are compared to see whether the means are different.

Describe the circumstances under which a confidence interval and hypothesis test yield the same results?