Testing a Claim about a Mean Difference Answers

Researchers wonder if practicing yoga reduces stress levels in adults. They select a random sample of 32 adults and assess their current stress levels. The participants are told to practice 60 minutes of yoga each day for one week. At the end of the week, their stress levels are assessed again. The mean difference (pre-yoga – post-yoga) in stress scores is 2.68 points with a standard deviation of 5.58 points. A positive value indicates that the subject’s stress level decreased.

A nurse at a local hospital wonders if the firstborn twin is taller than the second-born. He randomly selects the medical records of 33 sets of twins and finds the differences (firstborn – second-born) in the twins’ heights, in centimeters. The mean of the differences is 1.1 centimeters with a standard deviation of 2.3 centimeters. Assuming that the conditions for inference are met, what is the test statistic for testing the hypotheses ?

A statistics teacher is interested in whether there is a difference in the accuracy of dominant versus nondominant hands. She asks her students to roll a ball, once with each hand, toward a target. The students then measure the distance, in centimeters, between the ball and the target. Students will determine which hand they use first by tossing a coin. The differences (nondominant – dominant) in the distances for each student are listed.28, –33, 25, 41, –14, 21, 12, –30, 17, 26, 32, 27, –25, 18, 10, 22, –19, 4, 31, 19

An equestrian enthusiast is interested in the racing times of horses. She believes an older horse will have a faster race time than a younger horse. She selects a random sample of 17 sibling pairs of adult horses and records their times for running on the same track. The mean difference (older – younger) in the times to run the track is –15.7 seconds with a standard deviation of 8.3 seconds. Are the conditions for inference met?

Chuck wants to know which brand of tire, A or B, lasts longer on cars. He chooses 32 cars and puts brand A on one side of the car and brand B on the other side. The side that receives brand A is determined by a coin toss. After three months, Chuck measures the amount of tread on all tires to determine if, on average, there is a difference (brand A – brand B) in tread wear. What are the hypotheses Chuck should use?

A researcher is interested in whether parents and their children share the same opinion on topics. She selects a random sample of 31 pairs of mothers and their daughters. Each mother/daughter pair is shown a commercial and asked to rate the likelihood that they would purchase the product on a scale of 1 (not likely) to 5 (very likely). The mean difference (mother – daughter) of the ratings is 0.85 with a standard deviation of 1.59.

A music professor is interested in the effects of listening to music while memorizing a list of words. She asks 14 volunteers to memorize two different lists of words: one list while listening to music in the background and the other list with no music in the background. The order of the treatments is determined by a coin toss. The mean difference (music – no music) in the number of words memorized is 4.1 words with a standard deviation of 3.8 words. Assuming that the conditions for inference are met, what is the P-value for testing the hypotheses H0 :μdiff = 0; Ha :μdiff > 0?Find the t-table here.

Chuck wants to know which brand of tire, A or B, lasts longer on cars. He chooses 32 cars and puts brand A on one side of the car and brand B on the other side. The side that receives brand A is determined by a coin toss. After three months, Chuck measures the amount of tread on all tires to determine if, on average, there is a difference (brand A – brand B) in tread wear. Are the conditions for inference met?

A drug manufacturing company believes it has found a new medication to alleviate pain for headache sufferers. Twenty people with chronic headaches are asked to take a placebo pill or a pill containing the new medication during their next headache episode. The pill they take is determined by a coin flip. An hour later, the participants are asked to rate their headache pain level on a scale from 1 (no pain) to 5 (severe pain). During their next headache episode, the subjects are asked to take the other pill. The difference in pain ratings (new pill – placebo) is calculated for each subject. What are the hypotheses the company should use?

The principal of a large high school wants to improve student test scores, so he asks one of his science teachers to try a new method of teaching. Thirty-one students take a pretest on the first day of science class. After 6 weeks using the new instruction, the same students take a posttest. The mean difference (posttest – pretest) in scores is 4.8 points with a standard deviation of 9.7 points. Assuming the conditions for inference are met, what is the P-value for testing the hypotheses H0 :μdiff = 0; Ha :μdiff > 0?Find the t-table here.