Exam 9: Inferring Population Means

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. -Explain whether the confidence interval provides evidence that the mean catering cost of awedding has increased.

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

The reading level of a random sample of men and a random sample of women are measured. Researchers want know whether women typically read at a higher level than men.

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

Compare the normal distribution and the t-distribution. How are they similar? How arethey different?

Suppose that a major league baseball game has an average length of 2.9 hours with a standard deviation of 0.5 hours. It is known that game length is not normally distributed. Suppose a random sample of 36 games is taken from the population. Sketch the probability distribution and shade in the region that corresponds to the probability. What is the approximate probability that average game length will be greater than 3.1 hours? Round 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. -What is the standard error for the mean finish time of 30 randomly selected participants? Round to the nearest thousandth.

A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classical Music. Test the hypothesis that mood rating improved after being exposed to classical music. Following are the mood ratings for the four participants: Before exposure After exposure Participant \#1 4.0 5.0 Participant \#2 5.2 6.0 Participant \#3 3.2 4.0 Participant \#4 4.5 6.2 Assume that all conditions for testing have been met. Report the null and alternative hypothesis And p-value. At the 5% significance level, state 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 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. -Which of the following statements is not true about the t-distribution?

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 we were to make a histogram of the finishing times of the 30 participants in the 40-44 age group. Would the histogram be a display of the population distribution, the distribution of a Sample, or the sampling distribution of means?

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.

Describe the circumstances under which a confidence interval and hypothesis test 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 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 weight of King Salmon from Lake Michigan and Lake Superior are measured. Researchers want to know whether Lake Michigan King Salmon weigh less than those from Lake Superior.

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

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

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. -The weights at birth of five randomly chosen baby giraffes were 111, 115, 120, 103, and 106 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the Mean weight of all baby giraffes. 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. 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?

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 we were to make a histogram of the finishing times of all participants in the duathlon. Would the histogram be a display of the population distribution, the distribution of a sample, or The sampling distribution of means?

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followedby another 5 km run. The mean finish time of all male participants in a recent large duathlon was 1.54 hours with a standarddeviation of 0.22 hours. The distribution of finish times for males is right-skewed. Suppose that a sample of 30 randomlyselected male participants is selected. -Is the number 1.54 a statistic or parameter? Explain.