MATH 338: One-Sample Confidence Intervals and Hypothesis Testing - Prof. Sam Behseta, Lab Reports of Mathematics

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Testing

(1) A group of students were selected for a study on deriving ability. Initially the students were timed (in minutes) on a race course track under ideal weather conditions. Two days later the students were timed on the same course but under a rainy condition. The results of the time trials are listed below (assume that the population of time trials follow normal distribution): Student 1 2 3 4 5 6 7 8 9 Dry road 2.5 3.7 4.2 2.1 5.8 4.7 3.9 4.3 2. Wet road 3.1 3.2 4.7 3.9 5.1 6.2 4.1 4.8 2.

• Construct a 99% confidence interval for the difference in driving times of dry road con- ditions versus wet road conditions.
• Test the hypothesis that suggests the mean time trials under the two conditions are the same versus the mean time trials not the same. Carry out the test at α = 0.01 level.
• Carry out the same test at α = 0.05 level.

(2) Alcohol abuse has been described by college presidents as the number one problem on campus, and it is a major cause of death in young adults. How common is it? A survey of 13, students in U.S. four-year colleges collected information on drinking behavior and alcohol- related problems. The researchers defined binge drinking as having five or more drinks in a row for men and four or more drinks in a row for women. Frequent binge drinking was defined as binge drinking three or more times in the past two weeks. According to this definition, 3140 students were classified as frequent binge drinkers. Create a 95% confidence interval for the population proportion of frequent college binge drinkers. Test the hypothesis that suggests 23% of all college students are frequent binge drinkers.

(3) Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let μ be the true average refractometer reading for a new type of paint under consideration. A test of H 0 : μ = 20 versus Ha : μ > 20 based on a sample of 55 observations gave tobs = 3.2. What conclusion is appropriate at each of the following significance levels?

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(a) α = 0. 05 (b) α = 0. 01 (c) α = 0. 001

(4) A sample of 100 restaurant workers were asked whether or not work stress had a negative impact on their personal lives and 32 of them responded No. Test the hypothesis that for 25% of workers, stress has a negative impact on their lives.

(5) The restaurant worker survey in the previous example, found that 68 of a sample of 100 employees agreed that work stress had a negative impact on their personal lives. Construct a 95% confidence interval for the population proportion of all restaurant employees for whom work-related stress has a negative impact on their lives.

(6) A large university is interested in assessing student satisfaction with the overall campus environment. The plan is to distribute a questionnaire to an SRS of students, but before pro- ceeding, the university wants to determine how many students to sample. The questionnaire asks about a student’s degree of satisfaction with various student services, each measured on a five-point scale. The university is interested in the proportion p of students who declared satisfaction with the services in their questionnaires. The university wants to estimate p with 95% confidence and a margin of error less than or equal to 3%. For planning purposes, they are willing to use ˆp = 0.5 in their calculations. Find the required sample size to achieve the desired margin of error.