## A random variable is normally distributed with μ = 200 and σ = 60. Determine the mean and the standard error of the sampling distribution of the mean for simple random samples with the following sample sizes:

### statistics

##### Description

1.      (5 points) A random variable is normally distributed with μ = 200 and σ = 60.  Determine the mean and the standard error of the sampling distribution of the mean for simple random samples with the following sample sizes:

a.      n = 25

=                                                      =

b.      n = 100

=                                                      =

c.       n = 144

=                                                      =

2.      (5 points) Why is the central limit theorem so important to statisticians?

3.      (5 points) What is the difference between a point estimate and an interval estimate?

4.      (5 points) If the actual population mean μ = 15 and the interval estimate is between 12 and 18, does the interval estimate include the actual population parameter?  Circle the correct answer below.

YES                              NO                               NOT ENOUGH INFO

5.      (5 points) If the actual population mean μ = 15 and the interval estimate is between 19 and 23, does the interval estimate include the actual population parameter?  Circle the correct answer below.

YES                              NO                               NOT ENOUGH INFO

6.      (5 points) If the actual population mean µ = 15 and the sample mean  = 14, does the interval estimate include the actual population parameter?  Circle the correct answer below.

YES                              NO                               NOT ENOUGH INFO

7.      (5 points) If the actual population mean µ = 15 and the sample mean  = 45, does the interval estimate include the actual population parameter?  Circle the correct answer below.

YES                              NO                               NOT ENOUGH INFO

8.      (5 points) Set up the null and alternate hypotheses to test whether the population mean is equal to 10 when you have a sample mean.

H0:                                                                   Ha:

9.      (5 points) The 95% confidence interval of the population mean based on the sample data is (7, 11.5).  Would we reject or fail to reject the null hypothesis of problem #8 at the 95% level?  Circle the correct answer below.

REJECT                        FAIL TO REJECT                       NOT ENOUGH INFO

10.  (5 points) The 99% confidence interval of the population mean based on the sample data is (5.5, 13).  Would we reject or fail to reject the null hypothesis of problem #8 at the 99% level?  Circle the correct answer below.

REJECT                        FAIL TO REJECT                       NOT ENOUGH INFO