Paired t-tests

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.

• 1-sample t-test. The teacher should compare the sample mean for the girls against the population mean for the boys.

• Paired t-test. Since the boys and girls are in the same class, and are hence dependent samples, they can be linked.

• Either two-sample or paired t-test will work.

• Two-sample t-test. There is no natural pairing between the two populations.

• Paired t-test. Since there are 10 boys and 10 girls, we can link the two samples.

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.

• z-test, since the researcher can find the standard deviation of his population.

• Not enough information is given to determine the best type of test.

• Paired t-test, since there are two sets of measurements on the same subjects, providing a natural linking.

• Two-sample t-test, since how a subject performs with music should have no influence on how he performs without music, creating two independent samples.

• 1-sample t-test, since there is only one sample of subjects taking the dexterity tests.

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 99% confidence interval for the mean increase in yield.

• (-0.476, 6.726)

• (-6.726, -4.399)

• (-0.476, 4.399)

• (1.851, 6.726)

• (1.851, 4.399)

A coach uses a new technique in training middle distance runners. The times for 9 different athletes to run 800 meters before and after this training are shown. Construct a 99% confidence interval for the mean difference

• (-6.42, 8.87)

• (-0.76, 3.20)

• (-0.85, 3.29))

• (-0.54, 2.98)

• (-0.82, 3.27)

A high school coach uses a new technique in training middle distance runners. He records the times for 4 different athletes to run 800 meters before and after this training. A 90% confidence interval for the difference of the means before and after the training, μ_B - μ_A, was determined to be (2.6, 4.8).

• We know that 90% of all random samples done on runners at this high school will show that the mean time difference before and after the training is between 2.6 and 4.8 seconds.

• There is a 90% probability that a randomly selected middle distance runner at this high school will have a time for the 800-meter run that is between 2.6 and 4.8 seconds shorter after the training than before the training.

• Based on this sample, with 90% confidence, the average time for the 800-meter run for middle distance runners at this high school is between 2.6 and 4.8 seconds shorter after the new training.

• We know that 90% of the middle distance runners shortened their times between 2.6 and 4.8 seconds after the training.

• Based on this sample, with 90% confidence, the average time for the 800-meter run for middle distance runners at this high school is between 2.6 and 4.8 seconds longer after the new training.

Five students took a math test before and after tutoring. Their scores were as follows. Do the data suggest that there is a difference in the math scores? Perform a paired t-test at the 5% significance level.

• No, the data do not provide sufficient evidence to conclude that the tutoring has an effect on the math scores.

• Yes, the data do provide sufficient evidence to conclude that the tutoring has an effect on the math scores.