Name:______

AP Stats/ ______

Date: ______Date Due:______

AP Statistics

10.2 Homework Worksheet

Significance Tests: Comparing 2 Population Means

Please show all work on a separate piece of paper

1)Researchers equipped random samples of 56 male and 56 female students from a large university with a small device that secretly records sound from a random 30 seconds during each 12.5 minute period over two days. Then they counted the number of words spoken by each subject during each recording period and, from this, estimated how many words per day each subject speaks. The female estimates had a mean of 16,177 words per day with a standard deviation of 7520 words per day. For the male estimates, the mean was 16,569 and the standard deviation was 9108.

(a)Do these data provide convincing evidence of a difference in the average number of words spoken in a day by male and female students at this university? Carry out an appropriate test to support your answer.

(b)Describe a type I and type II error, what are the consequences for each?

2)How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good indicator of decay. Lower strength means the fabric has decayed. For one part of the study, the researcher buried 10 strips of polyester fabric in well-drained soil in the summer. The strips were randomly assigned to two groups: 5 of them were buried for 2 weeks and the other 5 were buried for 16 weeks. Here are the breaking strengths in pounds.

Group 1 (2 weeks) / 118 / 126 / 126 / 120 / 129
Group 2 (16 weeks) / 124 / 98 / 110 / 140 / 110

Do the data give convincing evidence that polyester decays more in 16 weeks than in 2 weeks?

3)The U.S Department of Agriculture (USDA) conducted a survey to estimate the average price of wheat in July and in September of the same year. Independent random samples of wheat producers were selected for each of the two months. Here are summary statistics on the reported price of wheat from the selected producers, in dollars per bushel.

Month / n / /
July / 90 / $2.95 / $0.22
September / 45 / $3.61 / $0.19

Construct and interpret a 99% confidence interval for the difference in the true mean wheat price in July and September.

In exercises 4 to 6 refer to the following setting. A study of roadrage asked random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each person was assigned a road rage score ona scale of 0 to 20. The participants were chosen by random digit dialing of phone numbers. The researchers performed a test of the following hypotheses::

4)Which of the following describes a type II error in the context of this study?

  1. Finding convincing evidence that the true means are different for males and females, when in reality the true means are the same
  2. Finding convincing evidence that the true means are different for males and females, when in reality the true means are different
  3. Not finding convincing evidence that the true means are different for males and females, when in reality the true means are the same
  4. Not finding convincing evidence that the true means are different for males and females, when in reality the true means are different.
  5. Not finding convincing evidence that the true means are different for males and females, when in reality the true means are different.

5)The P-value for the stated hypothesis is a 0.002. Interpret this value in the context of this study.

  1. Assuming that the rue mean road rage score is this same for males and females, there is a 0.002 probability of getting a difference in sample means.
  2. Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability of getting an observed difference at least as extreme as the observed difference.
  3. Assuming that the true mean road rage score is different for males and females, there is a 0.002 probability of getting an observed difference at least as extreme as the observed difference.
  4. Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability that the null hypothesis is true.
  5. Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability that the alternative hypothesis is true.

6)Based on the P-value in exercise 5, which of the following must be true.

  1. a 90% confidence interval for will contain 0
  2. a 95% confidence interval for will contain 0
  3. a 99% confidence interval for will contain 0
  4. a 99.9% confidence interval for will contain 0
  5. It is impossible to determine whether any of these statements is true based on the P-value.