#2.We wish to check that normal body temperature may be less than 98.6 degrees for a certainpopulation. In a random sample of 18 individuals from this population, the sample mean wasfound to be 98.217 and the samle standard deviation was 0.684. Assume the population isnormally distributed. Use a = 0.05.a. What are the null and alternative hypotheses?b. What hypothesis test should be used? (t-test or z-test)c. What is the rejection region?d. What is your test statistic? Is this statistic in the rejection region?e. What is the p-value of the test?f. What is your conclusion? Is there enough evidence to conclude that the normal bodytemperature is less than 98.6 degrees?g. What would be your conclusion under a = 0.01 level of significance? (use p-valuemethod) #1.The student senate at a large university feels that their seniors have a debt much less than $3,150,so it conducts a study of 50 randomly selected seniors and finds that the average debt is $2995,and the population standard deviation is $1100. Use a= 0.05 level of significance.a. What are the null and alternative hypotheses?b. What hypothesis test should be used? (t-test or z-test)c. What is the rejection region?d. What is your test statistic? Is this statistic in the rejection region?e. What is the p-value of the test?f. What is your conclusion? Can we support the student senate's claim using the datacollected?

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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 the math department chair at a large state university wants to estimate the average overall rating, out of five points, that students taking Introductory Statistics gave their lecturers on their end-of-term evaluations. She selects a random sample of 40 evaluations and records the summary statistics shown. Sample size Sample mean Sample standard deviation Population standard deviation Standard error Confidence level ? ?⎯⎯⎯ ? ? ??⎯⎯⎯⎯ ? 40 3.8303 1.0112 1.0750 0.1700 95% The department chair determines the standard error using ?, the standard deviation calculated from all student evaluations submitted to her department. Assume the Statistics lecturers' ratings have the same standard deviation. Use this information to find the margin of error and the lower and upper bounds of a 95% confidence interval for ?, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.
The mean income per person in the United States is $36,000, and the distribution of incomes follows a normal distribution. A random sample of 9 residents of Wilmington, Delaware, had a mean of $46,000 with a standard deviation of $8,400. At the 0.100 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?a. State the null hypothesis and the alternate hypothesis. b. State the decision rule for 0.100 significance level. (Round your answer to 3 decimal places.) c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) d. Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average at the 0.100 significance level?
You are a manager of a building that hosts the local farmers market for a town. You want to investigate if the average amount of sales for a vendor per week at your building is greater than $2040. After surveying 17 of their vendors, you find that mean sales per week of the vendors sampled was $2110 with a standard deviation of $114.03. What is the value of the test statistic for your hypothesis test? Note: 1- Only round your final answer. Round your final answer to two decimal places.
A developmental psychologist studies moral awareness in adolescents. Casual observation suggests that girls develop earlier than boys although most past research contains male participants. One test of moral awareness, standardized on male teens, has a mean of 72 and standard deviation of 18. The test is administered to 58 13-year-old girls, whose mean score is 76. Test the hypothesis that females test differently from males. binomial test Kruskal-Wallace H O one-sample t one-sample z
The average starting salary of students who graduated from colleges of Business in 2009 was $48,800. A sample of 100 graduates of 2010 showed an average starting salary of $50,000. Assume the standard deviation of the population is known to be $7000. We want to determine whether or not there has been a significant increase in the starting salaries. a. State the null and alternative hypotheses to be tested. b. Compute the test statistic. c. The null hypothesis is to be tested at the 5% level of significance. Determine the critical value for this test. d. What do you conclude from the test? e. What does the test result mean in the context of this problem?
An archer’s standard deviation for his hits is six (data is measured in distance from the center of the target). An observer claims the standard deviation is less.a. What type of test should be used?b. State the null and alternative hypotheses.c. Is this a right-tailed, left-tailed, or two-tailed test?
Milan
Grace Floral Shop claims that their average daily earnings is $497. An auditor wants to determine whether this claim is true. The auditor randomly selected a sample of 100 days and found that the sample mean earnings was $495 with a sample standard deviation of 9.75. Assist the auditor in conducting a hypothesis test, at the 3% level of significance, to determine whether the claim about their average daily earnings was overstated. d) Calculate the value of the test statistic for this test. e) Calculate the p-value for this test? f) State the conclusion of this test. Give reason for your answer.
You are a manager of a building that hosts the local farmers market for a town. You want to investigate if the average amount of sales for a vendor per week at your building is greater than $2050. After surveying 18 of their vendors, you find that mean sales per week of the vendors sampled was $2100 with a standard deviation of $101.08. What is the value of the test statistic for your hypothesis test? Note: 1- Only round your final answer. Round your final answer to two decimal places.
a. State the null and alternative hypothesis.

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