Basic Statistics Questions Using one sample mean

Here is an example of a statistics question you'll mostly find if you are enrolled in a basic statistics class. Hypothesis tests for this questions uses the one-sample z-test because the population standard deviation has been given.

Prep-Work Problem 11.1

ABC Auditors is investigating client response time when members of its staff follow up with clients requesting additional information. Currently, auditors claim that it takes more than five days for a client to respond with the requested information, To examine this claim, a partner at ABC Auditors asks a random sample of 10 employees to report the number of days it takes clients to respond to their inquiries. The following are the results of this random sample:
2,7,4,8,9,5,11,3,7,4
Can ABC Auditors conclude at the 5% significance level that it takes more than five days for a client to respond to inquiries assuming that the number of days is normally distributed with a standard deviation of 1.5?

Prep-Work Problem 11.2

Company X is a manufacturer that manufactures expensive computer components. The quality control manager has recently become frustrated with the number of components destroyed during the manufacturing process. He has told the CFO that the average assembly line worker destroys 12 or more components in a single shift. The quality control manager has informed this amount is unacceptable and these assembly line workers should be fired. The CFO is taking this complain seriously but thinks the number of destroyed items is less than what the quality control manager claims. In order to investigate the quality control manager’s claim, the CFO takes a random sample of 15 assembly line employees to see how many components are destroyed by each worker in a single shift. The sample is as follows:
1,14,8,15,17,10,12,6,14,21,15,9,11,4,8
Assuming that the number of destroyed items is normally distributed with a standard deviation of 3, can the CFO infer at the 10% significance level that the average number of destroyed components is less than 12?

Confidence Intervals and Hypothesis Testing
Questions 10 through 12 are based on hypothesis testing and confidence intervals. In the different textbooks you will find many criteria about when to use normal distribution and t distribution for solving these problems. Some of the criteria defined are based on approximation that when sample size is large, t distribution can be approximated to normal. However, here when you are using technology to solve problem, stick to criteria that when population standard deviation is known, normal distribution is used. In all other cases or respective of sample sizes, t distribution is used.
Q10) Consider variable overall satisfaction with the dining facility variable.
a. At 90% confidence, estimate the overall satisfaction with the fining facility.
b. At a 10% significance level, can we conclude overall satisfaction is different from 3.5? Explain criteria used to reach conclusion.
Q 11) Let’s perform analysis on satisfaction based on frequency of visit variable. You may find table completed in Question 4 useful for this analysis. At 5% significance level, test the hypothesis that those who visit dining facility daily are less satisfied that those who to not visit facility daily, In the answers provide test statistics, P value and conclusion. Use subscript 1 for daily visit and 2 for those who don’t visit dining facility daily.
This question is an example of inferential statistics that can be addressed by our expert writers.

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