# Basic Interval Statistics

Gorman Industries, LLC wants to give a short survey to a sample of hires who have been with the company for less than one year, roughly several thousand employees. They want to be able to establish a confidence interval for the proportion of new hires that are happy with Gorman Industries.

Plan 1: The HR manager will wait at the entrance as people are entering and leaving a quarterly employee communications meeting. Whenever he sees someone with a red badge, which indicates under one year with Gorman Industries, he will hand them a survey packet with instructions on completion.

Plan 2: E-mail new employees with the packet attached and request they complete it and e-mail it back within three days.

Which plan would you use and why?

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#### Solution Preview

The second plan is likely more reliable as long as you have a good response rate. Samples are usually evaluated by the process by which the participants were selected rather than by their final composition or size.

Plan 1 is a "convenience sample" or "accidental sample." That is, you would be getting all the new hires that attend the quarterly meetings. However, those that are sick, work at a remote location. Or those that are talking to someone and so you do not notice their badge. While this makes it easy to collect the data (convenient), those attending ...

#### Solution Summary

Your discussion is 345 words plus three references.

Basic Statistics Questions: Population mean, confidence interval, standard deviation, sample proportion, z-value, sample size

1. (TCO 7) Interpret a 99% confidence interval of (5.355, 5.445) for a population mean.

2. (TCO 7) A nursing school wants to estimate the true mean annual income of its alumni. It randomly samples 200 of its alumni. The mean annual income was $55,200 with a standard deviation of $1,500. Find a 95% confidence interval for the true mean annual income of the nursing school alumni. Write a statement about the confidence level and the interval you find.

3. (TCO 7) An auditor wants to estimate what proportion of a bank's commercial loan files are incomplete. The auditor randomly samples 80 files and finds 12 are incomplete. Using a 95% confidence interval, estimate the true proportion of incomplete files for ALL the bank's commercial loans. Write a statement about the confidence level and the interval you find.

1. (TCO 6) In the standard normal distribution, the standard deviation is always

0

1

2

none of these

2. (TCO 6) The area under a normal curve with mu = 15 and sigma = 2 is

0

1

2

none of these

3. (TCO 6) If Mary gets a 90 on a physics test where the mean is 85 and the standard deviation is 4.59, where does she stand in relation to her classmates?

She is in the top 15%.

She is in the bottom 15%.

She is in the top 5%.

She is in the bottom 5%.

4. (TCO 6) In a normal distribution with mu = 25 and sigma = 9, what number corresponds to z = -2?

21

16

7

none of these

5. (TCO 6) Let's assume you have taken 100 samples of size 49 each from a normally distributed population. Calculate the standard deviation of the sample means if the population's variance is 16.

0.571

0.429

0.327

0.107

6. (TCO 6) The area to the left of 'z' is 0.0681. What z-score corresponds to this area?

-1.40

1.49

-1.49

none of these

7. (TCO 6) Find P(9 < x < 15) when mu = 12 and sigma = 2.

0.9332

0.0668

0.8664

0.1336

8. (TCO 7) What is the critical z-value that corresponds to a confidence level of 88%?

approximately 1.48

approximately 1.55

approximately 1.75

approximately 2.11

9. (TCO 7) Compute the population mean margin of error for a 99% confidence interval when sigma is 4 and the sample size is 36.

+/- 1.3066...

+/- 1.0966...

+/- 1.7166...

none of these

10. (TCO 7) A standard IQ test has a mean of 98 and a standard deviation of 16. We want to be 90% certain that we are within 8 IQ points of the true mean. Determine the sample size.

27

11

10

none of these

11. (TCO 7) A private medical clinic wants to estimate the true mean annual income of its patients. The clinic needs to be within $100 of the true mean. The clinic estimates that the true population standard deviation is around $2,100. If the confidence level is 95%, find the required sample size in order to meet the desired accuracy.

1,695

2,100

1,432

1,700

12. (TCO 7) An auditor wants to estimate what proportion of a bank's commercial loan files are incomplete. The auditor wants to be within 4% of the true proportion when using a 95% confidence level. How many files must the auditor sample? No estimate of the proportion is available, so use 0.5 for the population proportion.

550

610

601

580