**Problem 1:**The owner of a gas station that conducts headlight inspections for the state is evaluating whether to continue offering the service. For the service to be profitable, the station needs to average more than 15 inspections per week. If the data does not strongly support this, the inspections will be discontinued. Over the past year (52 weeks), the data shows a sample average of 16.7 inspections per week with a sample standard deviation of 4.5. The question is whether this evidence is sufficient for the owner to justify retaining the inspection service. To determine this, the relevant hypotheses should be tested using the P-value method.

Answered: 1. The owner of a gas station which…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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4. Dougall compared the resting heart rate of average healthy citizens and soldiers suffering from post-traumatic stress disorder (PTSD). The normal resting heart rate for 25 healthy people averages 65 beats per minute (bpm) with a standard deviation of 6 bpm. The average heart rate of 16 people suffering from PTSD was 82 bpm with a standard deviation of 8 bpm. Use a = .05 for a two-tailed test. Does PTSD cause an elevation in resting heart rate? Complete all 4 steps of hypothesis testing.
A pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H0: μ = 50 versus Ha: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. The conditions for inference are met. The test statistic is t = –2.74 and the P-value is between 0.005 and 0.01. What conclusion should be made at the significance level, ? Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds. Reject H0. There…
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1. According to the records of an auto insurance company, the average distance that their customers drive to work is 17.4 miles. You are a new agent, and you think this is too low. You do a random polling of 50 of the company's customers, and you find that the average is 18.5 miles with a standard deviation of 3.4 miles. Do these data provide enough evidence at the 0.05 level of significance to conclude that the average distance driven to work is actually more than 17.4 miles? A. State the null and alternative hypotheses B. State the p-value. C. What is your conclusion about the null hypothesis? D. What is your conclusion in context of this problem?
The average credit card debt for a recent year was $8,776. Five years earlier the average credit card debt was $8,189. Assume sample sizes of 32 were used and the population standard deviations of both samples were $690. Is there evidence to conclude that the average credit card debt has increased?
1) Suppose you are a 20 year old student and you have convinced your parents to let you live off campus. Remarkably, they have agreed to pay for your housing. Suppose your parents claim that one-bedroom apartments cost an average of $600 per month. You disagree, and think one-bedroom apartments are more expensive than that. Suppose you went to the local paper and found 40 one-bedroom apartments listed. You calculate a sample mean of x = $600 with a standard deviation of ơ = $50. You and your parents have agreed on the a = .05level. a) State the null and alternative hypotheses. What is the critical value? Sketch a density curve and identify the b) critical region. oonaollingle to inot rovio (gaitea e bas OS- m olqme Stoaurgia.nb s ozA 20.0 c) Calculate the z value corresponding to the test statistic xand show its location on the sketch of part (b).
In one city, the average amount of time that tenth-graders spend watching television each week is 23 hours. The principal of Birchwood High School believes it is less for the 10th grade students that at his school. For a sample of 95 tenth-graders from the school, the mean amount of time spent watching television per week was 21.9 hours. Assuming a population standard deviation of 3.1 hours, does the data provide sufficient evidence to conclude that for all tenth-graders at Birchwood High school, the mean amount of time spent watching television per week is less than the city average of 23 hours? Perform the appropriate hypothesis test using a significance level of 0.005. What are the hypotheses? What is the test statistic? Is it a z or a t? Find the P-value for this test statistic. How does it compare to the significance level? On the normal curve, indicate the location of the test statistic and the p-value. (label them on the graph) Write…

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