# Hypothesis Testing: ANOVA, Chi-square, Two sample Z & T Test

For each problem below, answer the following

1. State the Ho

2. State the H1

3. Find the critical value

4. Determine the test statistic. Explain

5. State the decision rule

6. Show the decision rule graphically

7. Determine the computed value of the test statistic

8. Determine the p-value

9. What is your decision?

10. Interpret the decision

Problem 1

The City of Maumee comprises four districts. Chief of police Andy North wants to determine whether there is a difference in the mean number of crimes committed among the four districts. He recorded the number of crimes reported in each district for a sample of six days. At the .05 significance level, can the chief of police conclude there is a difference in the mean number of crimes?

Number of Crimes

Rec Center Key Street Monclova Whitehouse

13 21 12 16

15 13 14 17

14 18 15 18

15 19 13 15

14 18 12 20

15 19 15 18

Problem 2

The personnel director of Cander Machine Products is investigating 'perfectionism' on the job. A test designed to measure perfectionism was administered to a random sample of 18 employees. The scores ranged from 20 to about 40. One of the facets of the study involved the early background of each employee. Did the employee come from a rural background, a small city, or a large city? The scores are:

Rural Area 35 30 36 38 29 34 31

Small Urban Area 28 24 25 30 32 28

Large Urban Area 24 28 26 30 34

Problem 3

A six-sided die is rolled 30 times and the numbers 1 through 6 appear as shown in the following frequency distribution. At the .10 significance level, can we conclude that the die is fair?

Outcome Frequency

1 3

2 6

3 2

4 3

5 9

6 7

Problem 4

In a particular market there are three commercial television stations, each with its own evening news program from 6:00 to 6:30 P.M. According to a report in this morning's local newspaper, a random sample of 150 viewers last night revealed 53 watched the news on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13). At the .05 significance level, is there a difference in the proportion of viewers watching the three channels?

Problem 5

Two hundred managers from various levels were randomly selected and interviewed regarding their concern about environmental issues. The response of each person was tallied into one of three categories: no concern, some concern, and great concern. The results were:

No concern Some Great concern

Top management 15 13 12

Middle management 20 19 21

Supervisor 7 7 6

Group leader 28 21 31

Use the .01 significance level to determine whether there is a relationship between management level and environmental concern.

Quiz

Please, follow the 5-step procedure to solve the following problems - All work must be shown

1. NBC TV news, in a segment on the price of gasoline, reported last evening that the mean price nationwide is $1.50 per gallon for self-serve regular unleaded. A random sample of 35 stations in the Milwaukee, Wisconsin, area revealed that the mean price was $1.52 per gallon and that the standard deviation was $0.05 per gallon. At the .05 significance level, can we conclude that the price of gasoline is higher in the Milwaukee area? Determine the p-value.

2. Tina Dennis is the comptroller for Meek Industries. She believes that the current cash-flow problem at Meek is due to the slow collection of accounts receivable. She believes that more than 60 percent of the accounts are in arrears more than three months. A random sample of 200 accounts showed that 140 were more than three months old. At the .01 significance level, can she conclude that more than 60 percent of the accounts are in arrears for more than three months?

3. The Engineering Department at Sims Software, Inc., recently developed two chemical solutions designed to increase the usable life of computer disks. A sample of disks treated with the first solution lasted 86, 78, 66, 83, 84, 81, 84, 109, 65, and 102 hours. Those treated with the second solution lasted 91, 71, 75, 76, 87, 79, 73, 76, 79, 78, 87, 90, 76, and 72 hours. At the .10 significance level, can we conclude that there is a difference in the length of time the two types of treatment lasted?

4. There are two major Internet providers in the Colorado Springs, Colorado, area, one called HTC and the other Mountain Communications. We want to investigate whether there is a difference in the proportion of times a customer is able to access the Internet. During a one week period, 500 calls were placed at random times throughout the day and night to HTC. A connection was made to the Internet on 450 occasions. A similar one-week study with Mountain Communications showed the Internet to be available on 352 of 400 trials. At the .01 significance level, is there a difference in the percent of time that access to the Internet is successful?

#### Solution Summary

The solution provides step by step methods for the calculation of Z test for two populations. Formula for the calculation and interpretations of the results are also included. An interactive Excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.