Exam 24: Paired Samples and Blocks

A high school coach uses a new technique in training middle distance runners.He records the times for 4 different athletes to run 800 metres before and after this training.A 98% confidence interval for the difference of the means before and after the training, - ,was determined to be (2.5,4.7).

Suppose x is a variable on each of two populations whose members can be paired and that a paired difference is the difference between the values of the variable x on the members of a pair.True or false? The mean of the paired differences equals the difference between the two population means.

A researcher was interested in examining the difference in the number of hours of sleep married women and single women get each night.Five married women and five single women reported their average number of hours of sleep per night for the last week.Shown below is software output for two possible tests for the data. Which of these tests is appropriate for these data? Explain.Using the test you select,state your conclusion.

Ten different families are tested for the number of litres of water a week they use before and after viewing a conservation video.Do the data suggest that the mean amount after the viewing differs from the mean amount before the viewing? Perform a paired t-test at the 5% significance level.

Ten different families are tested for the number of litres of water they use each week before and after viewing a conservation video.We want to see if there is strong evidence that the conservation video changes people's water consumption rate.A t-test of the null hypothesis of no difference has a t-statistic of -2.894 with a P-value of 0.0178.Interpret this result by explaining the meaning of the P-value.

The table below shows the weights of 9 subjects,in kg,before and after they followed a particular diet for two months. Construct a 95% confidence interval for the mean difference of the "before" minus "after" weights if if (before-after)= 4.4333 and = 4.2146

A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys.She randomly selects 10 girls from the class and then randomly selects 10 boys.She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10.She does the same thing for the boys.

A researcher wishes to compare how students at two different schools perform on a math test.He randomly selects 40 students from each school and obtains their test scores.

The table below shows the weights of seven subjects before and after following a particular diet for two months. Do the data suggest that,on average,the diet is effective in reducing weight? Perform a paired t-test at the 1% significance level.

Ten different families were tested for the average number of litres of water they used per week before and after viewing a conservation video.A 95% confidence interval for the difference of the means after and before the training, - ,was determined to be (-10.3,-4.1).

A researcher was interested in comparing the salaries of female and male employees of a particular company.Independent random samples of 8 female employees (sample 1)and 8 male employees (sample 2)yielded the following weekly salaries (in dollars).

A study was conducted to determine if people consume more calories when they eat dinner while watching television.A random sample of ten people was selected to eat dinner one night in the dining room and the next night while watching television in the family room.The caloric content of their dinners was measured,and a 98% confidence interval for the difference in the means with and without the television, - μ,was determined to be (-80,220).

A researcher is interested in investigating whether people perform better at dexterity tests while listening to classical music or to no music.He designs a dexterity test,and first gives it to his participants while classical music is playing,and then while no music is playing.

The owner of a large apartment complex had an in-ground swimming pool installed in an effort to increase tenant satisfaction.Nine tenants were randomly selected to complete a questionnaire that assessed their level of satisfaction with the apartment complex.Their scores before and after the installation of the pool are shown.The owner wants to assess the effectiveness of the pool in increasing tenant satisfaction.

An agricultural company wanted to know if a new insecticide would increase corn yields.Eight test plots showed an average increase of 3.125 bushels per acre.The standard deviation of the increases was 2.911 bushels per acre.Determine a 90% confidence interval for the mean increase in yield.

A study was conducted to determine the average number of words children learn during their third year.For a random sample of one hundred children,parents reported the number of words spoken at 24 months and then again at 36 months of age.A 98% confidence interval for the difference of the means at 36 months and 24 months, - ,was determined to be (200,277).

Ten different families are tested for the number of litres of water they use each week before and after viewing a conservation video.We want to see if there is strong evidence that the conservation video reduces people's water consumption rate.A t-test of the null hypothesis of no difference has a t-statistic of -2.894 with a P-value of 0.0089.State your conclusion regarding the hypotheses.If this conclusion is incorrect,which type of error was made?

A coach uses a new technique in training middle distance runners.The times for 8 different athletes to run 800 metres before and after this training are shown below. Do the data suggest that,on average,the training helps to improve the athletes' times for the 800 metres? Perform a paired t-test at the 5% significance level.

Suppose that you wish to perform a traditional hypothesis test to test a claim regarding two means.Give an example of a situation in which the matched pairs test would be appropriate and give an example of a situation in which it would be appropriate to perform a two-sample t-test.

A consumer is interested in investigating the difference in price between regular and premium gasoline at major filling stations in the U.S.A..An independent,random sample of stations is chosen and the prices per gallon are recorded for regular and premium gasoline.A histogram or Normal probability plot of the differences would be needed to verify the Nearly Normal Condition.