Based on your answer in c, is the sample size large enough for the test procedures to

Psy. 5.35 A psychological experiment was conducted to investigate the length of time time delay between the administration of a stimulus and the observation of a specified reaction. A random sample of 36 persons was subjected to the stimulus and the time delay was recorded. The sample mean and standard deviation were 2.2 and .57 seconds, respectively. Is there significant evidence that the mean time delay for the hypothetical population of all persons who may be subjected to the stimulus differs from 1.6 seconds? Use a ⫽ .05. What is the level of significance of the test? 5.7 Inferences about M for a Normal Population, S Unknown 5.36 Set up the rejection region based on the t statistic for the following research hypotheses:

a. H

a : m ⬎ m , use n ⫽ 12, a ⫽ .05

b. H

a : m ⬍ m , use n ⫽ 23, a ⫽ .025

c. H

a : m ⬎ m , use n ⫽ 9, a ⫽ .001

d. H

a : , use n ⫽ 19, a ⫽ .01 5.37 A researcher uses a random sample of n ⫽ 17 items and obtains = 10.2, s ⫽ 3.1. Using an a ⫽ .05 test, is there significant evidence in the data to support H a : m ⬎ 9? Place bounds on the level of significance of the test based on the observed data. Edu. 5.38 The ability to read rapidly and simultaneously maintain a high level of comprehension is often a determining factor in the academic success of many high school students. A school district is considering a supplemental reading program for incoming freshmen. Prior to implementing the program, the school runs a pilot program on a random sample of n ⫽ 20 students. The students were thoroughly tested to determine reading speed and reading comprehension. Based on a fixed-length standardized test reading passage, the following reading times in minutes and in- creases in comprehension scores based on a 100-point scale were recorded. Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 n s Reading Time 5 7 15 12 8 7 10 11 9 13 10 6 11 8 10 8 7 6 11 8 20 9.10 2.573 Comprehension 60 76 76 90 81 75 95 98 88 73 90 66 91 83 100 85 76 69 91 78 20 82.05 10.88

a. Place a 95 confidence interval on the mean reading time for all incoming freshmen

in the district.

b. Plot the reading time using a normal probability plot or boxplot. Do the data appear

to be a random sample from a population having a normal distribution? c. Provide an interpretation of the interval estimate in part a. 5.39 Refer to Exercise 5.38. Using the reading comprehension data, is there significant evi- dence that the reading program would produce for incoming freshmen a mean comprehension score greater than 80, the statewide average for comparable students during the previous year? Provide bounds on the level of significance for your test. Interpret your findings. 5.40 Refer to Exercise 5.38. a. Does there appear to be a relationship between reading time and reading comprehen- sion of the individual students? Provide a plot of the data to support your conclusion.

b. What are some weak points in this study relative to evaluating the potential of the

reading improvement program? How would you redesign the study to overcome these weak points? Bus. 5.41 A consumer testing agency wants to evaluate the claim made by a manufacturer of discount tires. The manufacturer claims that its tires can be driven at least 35,000 miles before wearing out. To determine the average number of miles that can be obtained from the manufacturer’s tires, the agency randomly selects 60 tires from the manufacturer’s warehouse and places the tires on 15 cars driven by test drivers on a 2-mile oval track. The number of miles driven in thousands of miles until the tires are determined to be worn out is given in the following table. Car 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 n s Miles Driven 25 27 35 42 28 37 40 31 29 33 30 26 31 28 30 15 31.47 5.04 y y y m ⫽ m

a. Place a 99 confidence interval on the average number of miles driven, m, prior to

the tires wearing out. b. Is there significant evidence a ⫽ .01 that the manufacturer’s claim is false? What is the level of significance of your test? Interpret your findings. 5.42 Refer to Exercise 5.41. Using the Minitab output given, compare your results to the results given by the computer program. a. Does the normality assumption appear to be valid? b. How close to the true value were your bounds on the p-value?