STP 226Place Label Here.

EXAM #2 (100 points)

Material ch6-9

Instructor:

Honor Statement:

I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.

Signed ______

DIRECTIONS:

This is a closed book examination. You may use the formula card from the book (or a copy of it) and a calculator. Formula page should not have any notes on it. No hand written notes are permitted. Z-tables and t-tables are included at the end of the test.

There are 6 problems. Provide complete and well-organized answers.

Show your work!

1. Use the standard normal curve to find the following:

a.(6 points) area between - 1.54 and 1.73

b. (6points) z.15

c. (6points) third quartile of standard normal distribution

2. A random sample of size 9 was taken from the normally distributed population

with mean  = 150 and standard deviation  =18 .

Let denote the mean of this sample.

a. (6points) Name the sampling distribution of , give the mean and the

standard deviation of .

b. (6 points) Compute the probability that is less than 170:

P ( < 165)

3. The lifetime of a particular brand of fuse is normally distributed

with mean  = 1500 hours and standard deviation  = 100 hours.

a. (6 points) Sketch the distribution of that population and point out all

of its main features (shape, center, spread)

b. ( 6 points) What % of that brand of fuses has lifetime between 1400 and

1700 hours?

c. (6points) Let X be the lifetime of randomly selected fuse of that brand. Determine the following probability:

P(X > 1658)

d. (6 points) Determine the 25th percentile of the distribution of the lifetime of that brand of fuses.

4. You want to estimate the true mean weight of all the students at the large

university (  ) A random sample of 16 students gives a sample mean of 145 lb.

Assume that the weights of the students at that university are normally distributed with standard deviation of 15 lb.

a. (6points) Obtain 95% confidence interval for , the true mean

weight.

b. (6points) Looking at your interval, is the true mean likely to be

 = 131 lb or less? Clearly explain your answer.

c) (6 points) What sample size do you need in order to obtain 95% CI with a margin of error of at most 3 lb?

5. Consider the following:

You are testing the hypotheses:

H0 :  = 18 versus Ha :  > 18

You are using  = 0.05. Your test is based on a large random sample.

The population standard deviation  is known. The observed test statistic z = 1.78.

Use the above information to answer the following questions:

a. ( 6 points) What is the p- value for your test?

b. (6 points) Use your answer to part a) to decide if you reject H0 or not? Briefly explain your answer.

6. (16 points)The heights of young women in a general population in the USA have a mean of 67 inches, population standard deviation is unknown. A random sample of 4 women from Arizona gave heights , in inches, of:

63, 69, 62, 66

Do data present evidence at the significance level  =.10 that true mean height of women in Arizona is less than that of a general population in the USA?

Test appropriate hypothesis. Assume normal distribution of heights of the young women in Arizona.

  1. State null and alternative hypotheses, use appropriate symbols.
  1. Compute appropriate test statistics.
  1. Give rejection region, clearly mark critical value(s).
  1. Decide if null hypothesis should be rejected or not and give the reason why.
  1. Clearly explain your conclusion in words, answer question posed in the problem.