**MATH 221 Statistics for Decision Making ****Week 5 Homework **

MATH 221 Statistics for Decision Making Week 5 Homework

Question 1 From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.69 with a population standard deviation of 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues?

(19.24, 24.14)

(20.71, 22.67)

(21.78, 22.60)

(20.86, 22.52)

Question 2If a confidence interval is given from 43.83 up to 61.97 and the mean is known to be 52.90, what is the margin of error?

4.54

9.07

18.14

43.83

Question 3If a computer manufacturer needed a supplier that could produce parts that were very precise, what characteristics would be better?

wide confidence interval with high confidence level

narrow confidence interval at high confidence level

narrow confidence interval at low confidence level

wide confidence interval with low confidence level

Question 4Which of the following are most likely to lead to a wide confidence interval?

large sample size

small standard deviation

large mean

large standard deviation

Question 5If you were designing a study that would benefit from a narrow range of data points, you would want the input variable to have:

a small mean

a small sample size

a large standard deviation

a small margin of error

Question 6The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 57.06. What should be done about the production line?

Keep the line operating as it is outside the confidence interval

Stop the line as it is close to the confidence interval

Keep the line operating as it is close to the confidence interval

Stop the line as it is outside the confidence interval

Question 7In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 29.7 degrees and the population standard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer?

(29.16, 30.24)

(27.00, 32.4)

(24.30, 35.10)

(31.36, 32.44)

Question 8What is the 99% confidence interval for a sample of 52 seat belts that have a mean length of 85.6 inches long and a population standard deviation of 2.9 inches?

(84.4, 86.8)

(83.1, 88.1)

(84.6, 86.6)

(84.7, 86.5)

Question 9If two samples A and B had the same mean and sample size, but sample A had a larger standard deviation, which sample would have the wider 95% confidence interval?

Sample A as it has the larger sample

Sample B as it has the smaller sample

Sample B as its sample is more disperse

Sample A as its sample is more disperse

Question 10Why might a company use a lower confidence interval, such as 80%, rather than a high confidence interval, such as 99%?

It is cheaper as the sample size needs to be larger

It is faster as the sample size can be smaller

It is faster as more samples can be collected in a shorter time

It is cheaper as more samples can be collected

**APA Writing Checklist**

Use this document as a checklist for each paper you will write throughout your GCU graduate

program. Follow specific instructions indicated in the assignment and use this checklist to help ensure correct grammar and APA formatting. Refer to the APA resources available in the GCU Library and Student Success Center.

☐ APA paper template (located in the Student Success Center/Writing Center) is utilized for the correct format of the paper. APA style is applied, and format is correct throughout.

☐ The title page is present. APA format is applied correctly. There are no errors.

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**Scholarly Resources: **Scholarly resources are written with a focus on a specific subject discipline and usually written by an expert in the same subject field. Scholarly resources are written for an academic audience.

**Examples of Scholarly Resources include:** Academic journals, books written by experts in a field, and formally published encyclopedias and dictionaries.

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**Empirical Journal Article**: This type of scholarly resource is a subset of scholarly articles that reports the original finding of an observational or experimental research study. Common aspects found within an empirical article include: literature review, methodology, results, and discussion.

Adapted from “Evaluating Resources: Defining Scholarly Resources,” located in *Research Guides* in the GCU Library.

☐ The writer is clearly in command of standard, written, academic English. Utilize writing resources such as Grammarly, LopesWrite report, and ThinkingStorm to check your writing.

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