Module 6: Hypothesis Testing (One-Sample & Two-Sample Tests)

Module 6 Homework

Include your name on this submission. Answer each question. If the problem requires calculations or the use of excel, please include the equations, calculations, table number for the textbook appendix, or if using excel, copy and paste the excel formula used. Answers should be easily identifiable. Please include your name on the document when submitting to the dropbox.

Microsoft Excel was used on a set of data involving the number of defective items found in a
random sample of 46 cases of light bulbs produced during a morning shift at a plant. A
manager wants to know if the mean number of defective bulbs per case is greater than 20
during the morning shift. She will make her decision using a test with a level of significance
of 0.10. The following information was extracted from the Microsoft Excel output for the
sample of 46 cases:

n = 46

Arithmetic Mean = 28.00

Standard Deviation = 25.92

Standard Error = 3.82

Null Hypothesis: H0 :20

= 0.10

df = 45

T Test Statistic = 2.09

p-value = 0.021

One-Tail Test Upper Critical Value = 1.3006

Decision = Reject.

1. The parameter the manager is interested in is:
a) the mean number of defective light bulbs per case produced at the plant.
b) the mean number of defective light bulbs per case among the 46 cases.
c) the mean number of defective light bulbs per case produced during the morning shift.
d) the proportion of cases with defective light bulbs produced at the plant.

2. State the alternative hypothesis for this study.

3. What critical value should the manager use to determine the rejection region?

4. The lowest level of significance at which the null hypothesis can be rejected is ______.

A drug company is considering marketing a new local anesthetic. The effective time of the
anesthetic the drug company is currently producing has a normal distribution with a mean of
7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is
such that the effective time should be normally distributed with the same standard deviation,
but the mean effective time may be lower. If it is lower, the drug company will market the
new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36
results in a sample mean of 7.1. A hypothesis test will be done to help make the decision.

5. The appropriate hypotheses are:
a) H0 : 7.4 versus H1: 7.4
b) H0 : ≤7.4 versus H1: 7.4
c) H0 : ≥7.4 versus H1: 7.4
d) H0 : 7.4 versus H1: ≤7.4

6. For a test with a level of significance of 0.10, the critical value would be ________.

7. The value of the test statistic is ________.

8.The p-value of the test is ________.
9. At a 0.10 level of significance the null hypothesis should _________________.

A manufacturer produces light bulbs that have a mean life of at least 500 hours when the
production process is working properly. Based on past experience, the population standard
deviation is 50 hours and the light bulb life is normally distributed. The operations manager
stops the production process if there is evidence that the population mean light bulb life is
below 500 hours.

10. If you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10, the probability of a Type I error is _____ if the population mean bulb life is 510 hours.

11. If you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10, the confidence coefficient of the test is _____ if the population mean bulb life is 510 hours.

12. If you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05, the probability of the operations manager incorrectly stopping the process when the process is in fact working properly is _____.

13. If you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05, the probability of the operations manager not stopping the process when the process is in fact working properly is in fact below 500 hours is _____.

14. If you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01, the probability of the operations manager incorrectly stopping the process if the population mean bulb life is 510 hours is _____.

15. If you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01, the probability of the operations manager not stopping the process if the population mean bulb life is 510 hours is _____.

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t-test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below.

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

18

Sample Mean

99210

Sample Standard Deviation

13577

Population 2 Sample

Sample Size

12

Sample Mean

105820

Sample Standard Deviation

11741

Difference in Sample Means

-6610

t Test Statistic

-1.37631

t Test Statistic

Lower Critical Value

-1.70113

p-Value

0.089816

16. The researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. Which of the following is an appropriate alternative hypothesis?
a) H1 :females males
b) H1 :females males
c) H1 :females ≠ males
d) H1 :females males

17. The researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis, the correct test statistic is:
a) -6610
b) -1.3763
c) -1.7011
d) 0.0898

18. The researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is:
a) At the = 0.10 level, there is sufficient evidence to indicate a difference in the mean
starting salaries of male and female MBA graduates.
b) At the = 0.10 level, there is sufficient evidence to indicate that females have a lower
mean starting salary than male MBA graduates.
c) At the = 0.10 level, there is sufficient evidence to indicate that females have a higher
mean starting salary than male MBA graduates.
d) At the = 0.10 level, there is insufficient evidence to indicate any difference in the
mean starting salaries of male and female MBA graduates.

19. The researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?
a) Both populations of salaries (male and female) must have approximate normal distributions.
b) The population variances are approximately equal.
c) The samples were randomly and independently selected.
d) All of the above assumptions were necessary.

20. What is the 99% confidence interval estimate for the difference between two means?