Exam 24: Paired Samples and Blocks

Five students took a math test before and after tutoring.Their scores were as follows. Do the data suggest that the tutoring improves math scores on average? Perform a paired t-test at the 10% significance level.

A coach uses a new technique to train gymnasts.7 gymnasts were randomly selected and their competition scores were recorded before and after the training.The results are shown below. Do the data suggest that,on average,the training technique is effective in raising the gymnasts' scores? Perform a paired t-test at the 5% significance level.

A test of writing ability is given to a random sample of students before and after they completed a formal writing course.The results are given below.Construct a 99% confidence interval for the mean difference between the before and after scores if (before-after)= 2.0 and =2.6457

The violent crime rate (number of violent crimes per 100,000 residents)is investigated for ten Canadian cities for the years 1990 and 2000 to see if there has been a change.Shown below is software output for two possible tests. Which of these tests is appropriate for these data? Explain.Using the test you select,state your conclusion.

An agricultural company wanted to know if a new insecticide increases corn yields.Eight test plots showed an average increase of 3.125 bushels per acre when the insecticide was used compared to the previous year.The standard deviation of the increases was 2.911 bushels per acre.The company wants to use a paired t-test to determine the mean increase in yield.

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course.The results are given below.Construct a 95% confidence interval for the mean difference between the before and after scores if (before-after)= 3.7 and = 4.945

A researcher wants to investigate whether people can concentrate as effectively in the morning if they do not eat breakfast.He will score some volunteers on reading comprehension tests.Some of the testing will be done after volunteers have eaten breakfast,and some testing will be done after volunteers have skipped breakfast.Design an experiment that will require a two-sample t-test to analyze the results.Design an experiment that will require a matched pairs t-test to analyze the results.Which experiment would you consider to be the stronger design?

Ten different families are tested for the number of litres of water they use per week before and after viewing a conservation video.Construct a 90% confidence interval for the mean of the difference of the "before" minus the "after" times if (before-after)= 4.8 and =5.2451

A manufacturer has designed athletic footwear which it hopes will improve the performance of athletes running the 100-metre sprint.It wishes to perform a hypothesis test to compare the times of athletes at the 100 metres with these shoes and with their usual shoes.

The violent crime rate (number of violent crimes per 100,000 residents)is investigated for nine Canadian cities for the years 1990 and 2000 to see if there has been a change. Is there evidence that the violent crime rate has decreased? Suppose you had mistakenly treated these data as two independent samples instead of matched pairs.What would the significance test have found? Explain why the results are so different.

A coach uses a new technique in training middle distance runners.The times for 9 different athletes to run 800 metres before and after this training are shown below. Construct a 99% confidence interval for the mean difference of the "before" minus "after" times if (before - after)= 1.222 and = 1.826

A researcher wishes to determine whether listening to music affects students' performance on memory test.He randomly selects 50 students and has each student perform a memory test once while listening to music and once without listening to music.He obtains the mean and standard deviation of the 50 "with music" scores and obtains the mean and standard deviation of the 50 "without music scores".

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course.The results are given below.Do the data suggest that the mean score after the course differs from the mean score before the course? Perform a paired t-test at the 5% significance level.