1) A pharmaceutical company is marketing a new treatment for insomnia.They claim that their drug lengthens the average sleep of a person by 1.2 hours.You recruit 24 people to be in a random study of the treatment and give them themedicine. They report that their average sleep is lengthened by 1 hour. Thecompany says that the known standard deviation is 0.8 hours. Test the claim at thea = 0.05 level the claim that the medicine lengthens the average sleep of a personby 1.2 hours.

Given,sample size, n = 24sample mean, M = 1 hourpopulation standard deviation, .Claim:The medicine…

Answered: 1) A pharmaceutical company is…

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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Suppose that El Camino is studying the average number of hours students study for classes per week. According to research from 2010 El Camino students spent an average of 21 hours a week studying for classes. El Camino wants to study if this average has changed. To do this they take a random sample of 81 current students and find that the average student spent 19.3 hours studying with a standard deviation of 6.4 hours. (Note: You may assume there are approximately 20,000 El Camino students). (a) Carry out a hypothesis test at α = .05 to test the claim that the average number of hours per week that El Camino students study has changed since 2010. (b) Describe what it would mean in this situation to make a Type I error (c) Describe what it would mean in this situation to make a Type II error (d) Construct a 95% confidence interval for the average number of hours studied by El Camino students per week. Make sure to interpret your interval.
A survey reported that in a recent year, the mean serum cholesterol level in milligrams per deciliter for U.S. adults was 198 with a standard deviation of 43. A random sample of 110 adults was chosen. What is the probability that the mean cholesterol level is between 193 and 202?
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Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, µ, is less than 40 hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is 37 hours and that the standard deviation is 3 hours. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H ,) that should be used for the test? H:u is 7 In the context of this test, what is a Type I error? АТурe I error is 7 fact, u is 7 | the hypothesis that µ is ? when, in Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? ?
Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, u, is less than 40 hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is 35 hours and that the standard deviation is 3 hours. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? H: u is ? H: u is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? v the hypothesis that u is ? ? v. when, in Suppose that we decide to reject the null hypothesis. What sort of error might we be making? ?
In 2006, the Arundel County Maryland Department of Health tested local wells for elevated levels of arsenic. They found that 35 out of 71 wells showed elevated levels. Atomic Absorption Spectroscopy is a very convenient way to measure arsenic in water. Imagine you are a lab manager and you have given identical arsenic samples (n = 10) to two different technicians. The first technician determines his sample has a standard deviation of 0.015 while the second technician reports a standard deviation of 0.033. Construct a 90% confidence interval for the ratio of the sample standard deviations. Assume the population source data is normally distributed. Enter your answer using interval notation.
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It currently takes users a mean of 26 minutes to install the most popular computer program made by RodeTech, a software design company. After changes have been made to the program, the company executives want to know if the new mean is now different from 26 minutes so that they can change their advertising accordingly. A simple random sample of 37 new customers are asked to time how long it takes for them to install the software. The sample mean is 27.9 minutes with a standard deviation of 7.7 minutes. Perform a hypothesis test at the 0.05 level of significance to see if the mean installation time has changed. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.
The administrator at your local hospital states that on weekends the average wait time for emergency room visits is 10 minutes. Based on discussions you have had with friends who have complained on how long they waited to be seen in the ER over a weekend, you dispute the administrator’s claim. You decide to test your hypothesis. Over the course of a few weekends, you record the wait time for 40 randomly selected patients. The average wait time for these 40 patients is 11 minutes with a standard deviation of 3 minutes. Do you have enough evidence to support your hypothesis that the average ER wait time is different than 10 minutes? You opt to conduct the test at an α = 0.025 level of significance.
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