NAME: COMPREHENSIVE HOMEWORK PROBLEMS

03 Jun NAME: COMPREHENSIVE HOMEWORK PROBLEMS

Question
NAME:

COMPREHENSIVE HOMEWORK PROBLEMS

1 In thinking about doing statistical analysis, the sample mean should be interpreted as:

a a constant value that is equal to the population mean.

b a constant value that is approximately equal to the population mean.

c a random variable that is approximately equal to the population mean when sampling is done without replacement.

d a random variable that is approximately equal to the population mean if n > 30 and when sampling is done without replacement.

e a random variable that when averaged across many samples is approximately equal to the population mean.

2 Which of the following are random?

a x? after a sample is taken

b x? before a sample is taken

c µ after a sample is taken

d µ before a sample is taken

e More than one answer is correct.

3 The monthly earnings of teachers is normally distributed with a mean of $3,000 and the standard deviation of $250. We select a sample of 87 teachers. The sampling distribution of the sample mean has an expected value and standard deviation of:

a 3,000 and 26.8

b 3,000 and 1.69

c 3,000 and 250

d 3,000 and 2.87

e 3,000 and 321.6

4 The following data was collected by taking a simple random sample of a population

13 15 14 16 12

From this we know that,

a The population mean is 14.

b The point estimate of the population mean is 14.

c The population mean must be 14 since the sample mean is 14.

d Both a. and b. are correct.

e Both a., b., and c. are correct.

6 A quality control expert wants to test car engines. The production manager claims they have an average life of 92 months with a standard deviation of 8. If the claim is true, what is the probability that the mean engine life would be greater than 90.8 months in a sample of 93 engines?

a 0.0596

b 0.0735

c 0.4265

d 0.5596

e 0.9265

7 Increasing the size of a sample from 100 to 200 will

a reduce the standard error of the mean to one-half its original value.

b have no effect on the standard error of the mean.

c reduce the standard error of the mean to approximately 70% of its current value.

d double the standard error of the mean.

e None of the above answers is correct.

NEXT TWO ARE RELATED QUESTIONS ABOUT SAMPLING DISTRIBUTIONS.

One hundred samples of size 85 each are drawn from an unknown population distribution of x and a sample mean is calculated for each sample.

8 If the number of samples stays at 100, but the size of each sample is increased from 85 to 125, then one would expect the variation in sample means observed across samples to:

a increase.

b decrease.

c remain approximately the same.

d change a lot, but not necessary increase or decrease.

e be similar to the variation of x values in the population.

9 If the number of samples stays at 100, but the size of each sample is increased from 85 to 125, then one would expect the distribution of sample means observed across samples to:

a remain unknown.