# one sample confidence intervals and hypothesis testing assignment

**Part 1**

Use the random sampling method explained in the Instructor Perspective of Module 3 to

generate a random sample of size 45 from the given population. Then complete Table A in

the Q1 worksheet.

**Part 2**

Copy the sample obtained in Part 1 into the designated cells in the Q2 worksheet and

complete the following analysis of the data.

1. Complete Table A in the Q2 worksheet.

2. Use the sample to create 92%, 96% and 98% confidence intervals for the population

mean in the designated cells in Table B of the Q2 worksheet.

3. For each of the confidence intervals in step 2, use the information in Tables A and B

to determine the sample size needed to estimate the population mean to within .05

units. Do this in Table C of the Q2 worksheet.

In your report, explain your solution procedures and findings. Explain whether any of the

confidence intervals created in Step 2 does not contain the population mean.

**Part 3**

1. Use the random sampling method explained in the Instructor Perspective of Module 3

to generate a random sample of size 25 from the given population. Then complete Table

A in the Q3 worksheet.

2. Use the sample to create 92%, 96% and 98% confidence intervals for the population

mean in the designated cells in Table B of the Q3 worksheet.

In your report, explain your solution procedures and findings. Explain whether any of the

confidence intervals created in Step 2 does not contain the population mean.

**Part 4**

1. Use the random sampling method explained in the Instructor Perspective of Module 3

to generate a random sample of size 150 from the given population. Then complete

Table A in the Q4 worksheet.

2. Calculate the sample proportion of counties whose international migration rate (per

1000) is greater than 2 in cell I2.

3. Complete Table A in the Q4 worksheet.

4. Complete Table B, by using the sample to create a 90%, a 95%, and 99% confidence

intervals for the population proportion of counties whose international migration rate

(per 1000) is greater than 2 in the designated cells.

5. Complete Table C by determining the minimum sample size needed to estimate the

population proportion of interest to within 8%. Do this for each confidence interval

above. Assume that there is no prior knowledge about the proportion of counties whose

international migration rate (per 1000) is greater than 2.

6. Complete Table D.

In your report, explain your solution procedures and findings and state whether any of the

confidence intervals created in Step 4 above does not contain the population proportion of

interest.

**Part 5**

1. Use the random sampling method explained in the Instructor Perspective of Module 3

to generate a random sample of size 22 from the given population.

2. Complete Table A in the Q5 worksheet.

3. Use the sample to create 92%, 96% and 98% confidence intervals for the population

variance and standard deviation in the designated cells in Table B of the Q5 worksheet.

In your report, explain your solution procedures and findings. Explain whether any of the

confidence intervals created for the population standard deviation in Step 2 above does not

contain the population standard deviation.

**Part 6**

Use created sample in Q1 to test the hypothesis that the average migration rate (per 1000)

in the population is greater than 1. Use alpha = 0.05. Place results in the Q6 worksheet.

In your report, explain your hypothesis testing methods, procedures, and findings. In

particular, describe the meaning of the calculated P-value in the context of this problem.

**Part 7**

Use created sample in Q3 to test the hypothesis that the population average migration rate

(per 1000) is less than 1.5. Use alpha = 0.02. Place results in the Q7 worksheet.

In your report, explain your hypothesis testing methods, procedures, and findings.

**Part 8**

Use your created sample in Q4 to test the hypothesis that less than 20% of the US counties

have a migration rate that is higher than 2 (in 1000). Use alpha = 0.03. Place results in the

Q8 worksheet.

In your report, explain your hypothesis testing methods, procedures, and findings.

**Part 9**

Use your created sample in Q5 to test the hypothesis that the standard deviation of the

population emigration rates (in 1000) is different from 1.2. Use alpha = 0.05. Place results

in the Q9 worksheet.

In your report, explain your hypothesis testing methods, procedures, and findings.

**The report should include all your findings along with important statistical issues. The report should follow the following format:** (i) Introduction (ii) Analysis (iii) Conclusion