Estimating the Mean Difference Answers

A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table, and a dotplot of the differences is given.The researchers would like to construct a 99% confidence interval for the mean difference (A – B) in the time it took to experience relief. Are the conditions for inference met?

A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table.A 99% confidence interval for the mean difference (A – B) in the time it takes to experience relief is –8.37 minutes to 0.732 minutes. Based on the confidence interval, is it reasonable to claim that treatment A provides faster relief than treatment B?

To estimate the benefits of an SAT prep course, a random sample of 10 students enrolled in the course is selected. For each of these students, their entrance score on the exam taken at the beginning of the course is recorded. Their exit score on the exam they take at the end of the course is recorded as well. The table displays the scores.The mean of the differences is 193 points, and the standard deviation of the differences is 62.73 points. The conditions for inference are met. What is the correct 98% confidence interval for the mean difference (after – before) in score?Find the t-table here.

Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch.

Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch.

A doctor would like to estimate the mean difference in height of pairs of identical twins. The doctor randomly selects 8 pairs of identical twins and determines the current height, in inches, of each twin. The data are displayed in the table.A 95% confidence interval for the mean difference (twin 1 – twin 2) in height is (–0.823, 0.573). Based on the confidence interval, is it reasonable to claim there is no difference in the heights of twins?

To estimate the benefits of an SAT prep course, a random sample of 10 students enrolled in the course is selected. For each of these students, their entrance score on the exam taken at the beginning of the course is recorded. Their exit score on the exam they take at the end of the course is recorded as well. The table displays the scores.A 98% confidence interval for the mean difference (after – before) in score is 137.04 points to 248.96 points. Based on the confidence interval, is it reasonable to claim that the SAT prep course is beneficial?

A group of six students decides to conduct an experiment about "brain freeze,” a phenomenon that often occurs when eating something cold. The students each flip a coin. If they flip heads, they eat a cup of Italian ice as fast as they can while sitting in an air-conditioned car. If they flip tails, they eat a cup of Italian ice as fast as they can while sitting outside in the sunshine. After a recovery period, they each complete the opposite treatment. The students record the amount of time it takes, in seconds, for them to experience brain freeze under each condition.

A cell phone manufacturer would like to estimate the mean difference in battery lifespan for a phone in full-power versus power-saver mode. They randomly select eight phones and determine the battery lifespan, in hours, for each phone using each power mode.A 90% confidence interval for the true mean difference (low power battery life – full power battery life) in battery life is 5.42 hours to 6.71 hours. A journalist claims that battery lifespan is, on average, 5 hours longer when the phone is used under low-power mode as opposed to full-power mode. Is this claim supported by the 90% confidence interval?

To estimate the benefits of an SAT prep course, a random sample of 10 students enrolled in the course is selected. For each of these students, their entrance score on the exam taken at the beginning of the course is recorded. Their exit score on the exam they take at the end of the course is recorded as well. The table displays the scores.What is the mean difference (after – before) and the standard deviation of the differences?