Statistics - Hypothesis Testing Projects

A sample of 64 observations is selected from a normal population. The sample mean is 215, and the sample

Problem: A sample of 64 observations is selected from a normal population. The sample mean is 215, and the sample standard deviation is 15. Conduct the following test using the 0.03 significance level.

\[\begin{aligned} & {{H}_{0}}:\mu \ge 220 \\ & {{H}_{A}}:\mu <220 \\ \end{aligned}\]

Problem: The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

Problem: At the time she was hired as a server at the Grumney Family Restaurant, Beth Bridgen was told: "You can average more than $20 a day in tips". Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $24.85, with a standard deviation of $3.24. At the 0.01 significance level, can Ms. Bridgen conclude that she’s earning more than $20 in tips, on the average?

Problem: The following hypotheses are given:

\[\begin{aligned} & {{H}_{0}}:\mu =0.40 \\ & {{H}_{A}}:\mu =0.40 \\ \end{aligned}\]

A sample of 120 observations revealed that p = 0.30. At the 0.05 significance level, can the null hypothesis be rejected?

15. Given the following hypotheses:

\[\begin{aligned} & {{H}_{0}}:\mu \le 10 \\ & {{H}_{A}}:\mu >10 \\ \end{aligned}\]

For a random sample of 10 observations, the sample mean was 12 and the sample standard deviation was 3. Using the 0.05 significance level:

State the decision rule
Compute the value of the test statistics
What is your decision regarding the null hypothesis?

18. The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

Problem: As part of a study of corporate employees, the director of Human Resources for PNC, Inc. wants to compare the distance traveled to work by employees at their office in downtown Cincinnati with the distance for those in down town Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month, with a standard deviation of 30 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month, with a standard deviation of 26 miles per month. At the .05 significance level, is there a difference in the mean number of miles traveled per month between Pittsburgh and Cincinnati employees? Use the 5 step Hypothesis-test procedure.

6. Mary Jo Fitzpatrick is the Vice President for Nursing services at St. Luke’s Memorial Hospital. Recently she noted that in the job postings for nurses that those that are unionized seem to offer higher wages. She decided to investigate the issue and gathered the following sample:

Group Mean St. Dev Sample Size

Union $20.75 $2.25 40

Nonunion $19.80 $.90 45

Would it be reasonable to conclude that union nurses make more? Use 0.02 significance level.

Problem: The null hypothesis and alternate hypothesis are:

H ₀ : ${{\mu }_{d}}$ = 0

H ₁ : ${{\mu }_{d}}$ ≠ 0

The following paired observations show the number of traffic citations given for speeding by Office Dhondt and Officer Meredith of the South Carolina Highway Patrol for the last five moths

Day
	May	June	July	August	September
Officer D.	30	22	25	19	26
Officer M	26	19	20	15	19

At the .05 significance level, is there a difference in the mean number of citations given by the two officers? Use the 5 step Hypothesis-test procedure.

Problem: The following is sample information. Test the hypothesis at the .05 significance level the treatment means are equal.

Treatment 1	Treatment 2	Treatment 3
9	13	10
7	20	9
11	14	15
9	13	14
12		15
10

State the Null hypothesis and the alternate hypothesis
What is the decision rule
Compute SST, SSE, and SS Total
Compare the ANOVA table
State your decision regarding the null hypothesis

Problem: A real estate developer is considering investing in a shopping mall on the outskirts of Atlanta. Three parcels of land are being evaluated. Of particular importance is the income in the area surrounding the proposed mall. A random sample of four families is selected near each proposed mall. The results are shown below. At th e0.05 significance level, can we conclude that there is a difference in the mean income?

Problem: Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

Treatment 1	Treatment 2	Treatment 3
3	9	6
2	6	3
5	5	5
1	6	5
3	8	5
1	5	4
	4	1
	7	5
	6
	4

State the Null hypothesis and the alternate hypothesis
What is the decision rule?
Compute SST, SSE, and SS Total
Compare the ANOVA table
State your decision regarding the null hypothesis
If Ho is rejected, can we conclude that treatment 2 and treatment 3 differ? Use the 95 percent level of confidence

Problem: There are three hospitals in the Tulsa Oklahoma area. The following data show the number of outpatient surgeries performed at each hospital last week. At the .05 significance level, can we conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week?