Statistics Review for Final Exam (2nd set)
(Chapter 6, 7, and 8)

 

Last time updated: 4/25/2012 10:15AM

1. In a New York modeling agency, a researcher wishes to see if the average height of female models is really less than 67 inches, as the chief claims. A sample of 30 models has an average height of 66.8 inches. The standard deviation of the population is 1.7 inches. At = 0.05, is the average height of the models really less than 67 inches? Use the P-value method.

Answer:

 

Ho: = 67
H1: < 67 (claim)

Z =

  Area = 0.2578

 

p = 0.2578

 

Since p > , do not reject Ho.

 

There is not enough evidence to support the claim that the average height of the models is less than 67 inches.

 

2.  A magazine article stated that the average age of women who are getting married for the first time is 26 years. A researcher decided to test this hypothesis at =0.01. She selected a sample of 25 women who were recently married for the first time and found the average was 25.1 years. The population standard deviation was 3 years. Should the null hypothesis be rejected?

Answer:

Ho: =26 (claim)
H1: 26

Since is known, use Z test.

(Draw the figure yourself)

Critical value Zc = +2.58

Z = ;

 

Do not reject Ho since Z falls within the non-rejection region.

The null hypothesis should not be rejected on the basis of the sample. (Alternative summary: There is not enough evidence to reject the claim)

 

3. Membership in an elite organization requires a test score in the upper 30% range. If the variable is normally distributed with = 115 and = 12, find the lowest acceptable score that would enable a candidate to apply for membership.

Answer:

x = 121.24 = 121

The lowest acceptable score is 121.

 

4. A researcher wishes to estimate within $300 the true average amount of money a county spends on road repairs projects each year. If she wants to be 90% confident, how large a sample is necessary? The population standard deviation is known to be $900.

Answer:  n = 25

 

5. For a certain urban area, in a sample of 5 months, an average of 28 mail carriers were bitten by dogs each month. The standard deviation of the sample was 3. Find the 90% confidence interval of the true mean.

Answer:

      25<<31

 

6. A random sample of 49 shoppers showed that they spend an average of $23.45 per visit at the Saturday Mornings Bookstore. The standard deviation of the population was $2.80. Find a point estimate of the population mean. Find the 90% confidence interval of the true mean.

Answer:

Point estimate: = $23.45 

Interval estimate: $22.79 <  < $24.11

 

7. The average repair cost of a microwave oven is $55, with a standard deviation of $8. The costs are normally distributed. If 12 ovens are repaired, find the probability that the mean of the repair bills will be greater than $60.

Answer:

P (>$60) = 0.015

 

8. The average salary for graduates entering the business field is $40,000. If the salaries are normally distributed with a standard deviation of $5000, find the probability that

 

a. An individual graduate will have a salary over $45,000.

Answer: P(x>$45,000) = 0.1587

 

 b. A group of nine graduates will have a group average over $45,000.
Answer: P(>$45,000) = 0.0013

 

9. Drivers of a taxi company have an average of 12.4 years’ experience. In a study of 15 taxi drivers, the average experience was 11.2 years and the samples standard deviation was 2. At =0.10, test the claim that the number of years’ experience of the taxi drivers is less than 12.4 years.

Answer:

Ho: = 12.4
H1: < 12.4 (claim)

It’s a t test because  is unknown.

(Draw figure yourself)

Critical value tc = -1.345

t =

 

Reject Ho.

There is enough evidence to support the claim that the average experience of the company’s drivers is less than 12.4 years’ experience.