The director of a state agency believes that the average starting salary for clerical employees in the state is less than $31,000 per year. To test the hypothesis, the director has collected a simplerandom sample of 100 starting clerical salaries from across the state and found that the sample mean is $30,650.a. State the appropriate null and alternative hypotheses.b. Assuming the population standard deviation is known to be $1,500 and the significance level for the test is to be 0.005, what is the critical value (stated in dollars)?c. Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis?d. Referring to your answer in part c, which of the two statistical errors might have been made in this case? Explain.a. State the appropriate null and alternative hypotheses. Choose the correct answer below.A. Ho: 231,000HAH<31,000OD. Ho: H≤30,650HAH>30,650b. Find the critical value, in dollars.(Round to the nearest cent as needed.)OB. Ho μ230,650HAH<30,650OE. Hous31,000HA: H>31,000CEEBOC. Ho: H=31,000Hx: μ # 31,000OF. Ho H=30,650HA: H#30,650

As per the state agency's director's belief, the clerical employees' average starting salary is less…

Answered: The director of a state agency believes…

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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A report states that the mean yearly salary offer for students graduating with mathematics and statistics degrees is $62,915. Suppose that a random sample of 50 mathematics and statistics graduates at a large university who received job offers resulted in a mean offer of $63,200 and a standard deviation of $3,700. Do the sample data provide strong support for the claim that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,915? Test the relevant hypotheses using a = 0.05. USE SALT Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t = P-value = State your conclusion. O Reject Ho. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,915. Fail to reject H. We have convincing evidence that the…
1. Find the test statistic 2. Identify the P-Value
In order to study the amounts owed to the city council, a city clerk takes a random sample of 16 accounts from a large number of delinquent accounts and finds the average amount owed to the city to be $258. It has been claimed that the true mean amount owed on accounts of this type is greater than $250. If it is appropriate to assume that the amount owed is a normally distributed random variable with a standard deviation of $33, then the value of the test statistic appropriate for testing the claim is: (Your answer should be correct to two decimal places.)
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?
A manufacturer claims that only 2% of their products are defective. A store receives a delivery of 300 items from the manufacturer. Let p-hat = the proportion of defective items in a sample of 300 items. Assuming the manufacturer is correct that only 2% of their products are defective, what are the mean and standard deviation of the sampling distribution of p-hat ? Options: The mean is 0.02 and the standard deviation is 0.008. The mean is 6 and the standard deviation is 2.42. The mean is 6 and the standard deviation is 5.88. The mean is 0.02 and the standard deviation is 0.196.
I would like to test the hypothesis that the average round trip airfare between Phoenix and San Diego is higher for a flight originating in Phoenix when compared to a flight originating in San Diego. The following data summarizes the sample statistics for round trip flights originating in both cities. Originating City Phoenix San Diego Sample mean $240 $160 Sample size 18 18 Sample standard deviation $70 $40 If Population 1 is defined as flights originating in Phoenix and Population 2 is defined as flights originating in San Diego, the 90% confidence interval for the difference in population means is O ($50.20, $109.80) O ($42.80, $117.20) ($47.80, $112.20) O ($51.80, $108.20)
2. University researchers claim that the average enrollment at four-year colleges is higher than two-year community colleges. Two surveys are undertaken at 35 four-year universities and 35 two-year colleges. The mean enrollment at the four-year institutions was 5,466 with a standard deviation of 8,191. The average enrollment at the two-year schools was 5,068 with a standard deviation of 4,777. Using a 95% confidence level, are the findings of the surveys consistent with the university researchers’ claim? 2. Does the null hypothesis reject H0 or fail to reject H0?
1. A random sample of 50 students in Holy Angel University shows that they spend an average of 3 hours per day on social media apps with a standard deviation of 0.5 hours. Assume a normal distribution. Construct a 90% and 97% confidence interval for the average number of hours spent on social media apps per day.
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?
Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,800 houses. The subdivision was built in 1983. A sample of 110 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $229,000, with a standard deviation of $8,500, what is the probability that the sample average is greater than $231,000? Appendix A Statistical Tables (Round the values of z to 2 decimal places, e.g. 15.25. Round your answer to 4 decimal places, e.g. 0.2513.)enter probability rounded to 4 decimal places
5. The ages of U.S. commercial aircraft have a mean of 13 years and a standard deviation of 7.9 years (based on data from Aviation Data Services). a. If the Federal Aviation Administration randomly selects 35 commercial aircraft for special stress tests, find the probability that the mean age of this sample group is greater than 15 years? b. If the Federal Aviation Administration randomly selects 42 commercial aircraft for special stress tests, what is the mean sample age of the aircraft for the top 75% of the sample?4

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