Question

In a July 2001 research note, the U.S. Department of Transportation reported the results of the National Occupant Protection Use Survey. One focus of the survey was to determine the level of cell phone use by drivers while they are driving a motor passenger vehicle. Data collected by observers at randomly selected intersection across the country revealed that in a sample of 1165 drivers, 35 were using their cell phone.

(a) Check and verify the two conditions for a 98% confidence interval.

(b) Compute a 98% confidence interval for the proportion of drivers that are using their cell phones. Show the set-up for the interval.

There are many ways to measure the reading ability of children. Research designed to improve reading performance is dependent on good measures of the outcomes. One frequently-used test is the DRP, or Degree of Reading Power. It is known that the distribution of DRP scores is normally distributed. A researcher suspects that the mean score µ of all third-graders in Henrico County Schools is different from the national mean, which is 32. To test her suspicion, she administers the DRP to a random sample of 22 Henrico County third-grade students. Their scores are recorded in the following table:

40 26 39 17 42 18 24 43 46 27 19

47 19 26 37 34 15 45 41 39 31 46

(a) Find the t critical value for a 90% confidence interval for the true mean, µ, of the population.

(b) State and verify the conditions for the confidence interval.

(c) Compute and interpret the 90% confidence interval for the mean DRP score in Henrico County Schools. (You can find your point estimate and standard error in your calculator using the 1-Var Stats function. Compare your answers with a classmate to make sure you entered things in correctly!)

(d) Use the confidence interval you constructed in Part (c) to comment on whether you agree with the researcher’s suspicion. Explain your reasoning clearly.

Answer 1

The researcher suspicion that the mean score µ of all third-graders in Henrico County Schools is different from the national mean, which is 32 is not valid since 32 lies in the 90% confidence interval.