Exam 13: Asking and Answering Questions About the Difference Between Two Means

The data below give the weights in ounces of randomly-selected bars of bath soap produced by two different molding machines. The question of interest is whether these two molding machines produce soap bars of differing average weight. Find the P-value for the this test assuming that the weights for the two machines are approximately normal..

Suppose 8 adult patients with the same diagnosis were randomly selected. Researchers want to check whether the injected medication will affect the change in body temperature. The patient's body temperature was measured before and after the injected medication and resulting data are given in the accompanying table. ​ Construct and interpret a 95% confidence interval estimate for the difference in mean temperature before and after the injected medication.

The researchers suggested that the time of the second race in karting is less than during the first race because a person remembers the track. Suppose 8 adults were randomly selected. The time spent on the first and second race was recorded for each person from the sample and resulting data are given in the accompanying table. Do these data support the claim that the mean difference in time spent on the first and second race is greater than zero? Use a randomization test to select the appropriate output for one set of 1000 simulated sample differences in means and carry out a hypothesis test for a difference in means.

Researchers assessed the effectiveness of courses on logic and computer thinking for adult residents of the city. 10 adults were tested on the topic of logic and computer thinking before and after the courses, their knowledge was evaluated on a scale of 0 to 20. The resulting data are given in the accompanying table. Assume that the sample of 10 adults is representative of adult residents of the city. ​ Construct and interpret a 90% confidence interval estimate for the difference in the mean score before and after courses on logic and computer thinking.

When creating a confidence interval involving treatment proportions in an experiment, the interpretation of the confidence interval estimate should be worded in terms of what quantities?

Samples from two independent, normally-distributed populations produced the following results. Calculate the 95% confidence interval for the difference between population means, µ₁-µ₂