1. The records of SCA Registrar show that the average final grade in Mathematics forSTEM students is 91 with a standard deviation of 10. A group of student-researchersfound out that the average final grade of 37 randomly selected STEM students inMathematics is no longer 91. Use 0.05 level of significance to test the hypothesis.A. State the hypotheses.B. Determine the test statistic to use.C. Determine the level of significance, critical value, and the decision rule.D. Compute the value of the test statistic.E. Make a decision.F. Draw a conclusion.

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Answered: 1. The records of SCA Registrar show…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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.
11. The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 2.1 calls. Using the .05 significance level, can we conclude that the mean number of calls per salesperson per week is more than 4O?
2. A professional racing team is holding tryouts at its test track. The team requires its drivers to have an average lap time of at most 133 seconds at its test track. The team will use a one sample z-test of significance to determine if they should hire a new driver. An amateur driver completes 10 timed laps of the test track with an average lap time of 140 seconds. If the standard deviation of all lap times at this track is 4.5 seconds, what is the value of the test statistic? Round your answer to two decimal places. Answer value Please show work!!!
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?
a. Identify the null and alternative hypotheses Choose the correct answer below
1. What is the quantile for significance level 0.1 and 0.01 in both two and one tailed test? 2. A principal at a school claims that the students in his school are above average intelligence. A random sample of thirty students' IQ scores have a mean score of 112.5. Is there sufficient evidence to support the principal's claim? The average IQ is 100 with a standard deviation of 15. Use a = 0.05
6. You randomly select and weigh 27 samples of an allergy medication. The sample standard deviation is 1.22 milligrams. Assuming the weights are normally distributed, construct 90% confidence intervals for the population variance and standard deviation. Please interpret your result.
4. The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750. a. a) State the appropriate null and alternative hypotheses. b) Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the critical value (stated in dollars)?
An experiment was run to compare three groups. The sample sizes were 28, 33, and 102, and the corresponding estimated standard deviations were 2.7, 2.6 and 4.8. 1) What is the value of the pooled standard deviation? 2) Explain why the answer for part 1 is much closer to the standard deviation of the third group than to either of the other two standard deviations.
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?
A . please do not uplod handwritting image ( only typing please)
In 2017, the SAT was scored out of 1600. The average SAT scores among the 925 Texas students who stated their intended major was Mathematics was 1148. The average SAT score among the 1026 Texas students who stated their intended major was History was 1031. Assume the true standard deviation for both populations is 193. (a.) Test the hypothesis at the 1% significance level that future Texas math majors had a higher SAT score on average in 2017 than future Texas history majors. (b.) Find a 98% confidence interval for the difference in their SAT scores (Let μ1 be the mean math major score and μ2 be the mean history major score).

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