Rounding. Round your z-scores to two decimal places when using a normal distribution table and the areas under the normal curve to decimal places. When using the t-distribution or doing other calculations, round to 3 decimal places unless otherwise directed. Do not round until the last step of your calculations (Note: see FAQ 4.2).

Testing claims. To avoid loss of points, you must include all 5 parts listed below whenever you are asked to test a claim or conduct a hypothesis test.

1. State the null hypothesis, 0, and the alternate hypothesis, , indicating which is the claim.
2. Show the calculation of the test statistic.
3. Depending on the method you use, list either (a) the p-value or (b) find the critical value(s). Note: One tail tests have only one critical value, but two tail tests have two.
4. State decision whether to reject or "fail to reject" the null hypothesis, 0.
5. State your conclusion about the claim. You should use the wording suggested by the author in section 7.1.

Problem 1

Tea consumption. A researcher claims that the numbers of cups of tea that persons drink per day are distributed as shown in Table 1, Part A. You randomly select 1960 persons and use a survey to ask the question, "How many cups of did you drink today?". The results of the survey are shown in Table 1, Part B. At =0.05, test the researcher's claim.

Part A	---	Part B
Response	%	Response	f
0 Cups	33%	0 Cups	659
1 Cup	27%	1 Cup	519
2 Cups	18%	2 Cups	367
3 Cups	14%	3 Cups	295
4 or more	8%	4 or more	120

Problem 2

Test scores. A teacher claims that test scores are distributed as shown in Table 2, Part A. You randomly select 660 tests. The distribution of the test scores is shown in Table 2, Part B. At =0.01, test the teacher's claim.

Part A	---	Part B
TestScores	%	TestScores	f
0 to 59	5%	0 to 59	39
60 to 69	14%	60 to 69	82
70 to 79	32%	70 to 79	193
80 to 89	35%	80 to 89	267
90 to 100	14%	90 to 100	79

Problem 3

Testing normality. At =0.01, use the chi-square goodness of fit test to test the claim that the data in Table 3 are normally distributed. Carefully read the document, Testing Data for Normality, posted in the unit 5 folder. In the Excel files folder under Files in Course Information, you can find a sample Microsoft Excel spreadsheet that shows how to use the Chi-square Goodness-of-Fit test to test for normality. I suggest that you download the sample spreadsheet. If you double-click a cell Microsoft Excel will display the formula. To exit the formula view, remember to enter Esc, other wise you could overwrite the contents of the cell. You should also review the method for finding the mean of a frequency distribution (section 2.3) and the method for finding the standard deviation of grouped data (section 2.4).

Class Boundaries	Frequency
Lower	Upper
203.5	223.5	39
223.5	243.5	123
243.5	263.5	352
263.5	283.5	287
283.5	303.5	174
303.5	323.5	25

Problem 4

A researcher who is interested in the reasons why students choose to continue education wants to know whether the reason for continuing their education is related to job type. Table 4 shows the results of a survey randomly administered to the students. At =0.01is there enough evidence to support the claim that the reason and the type of job are dependent?

Type ofWorker	Reason for Continuing Education
Professional	Personal	ProfessionalandPersonal
Technical	93	41	36
Other	78	87	34

Problem 5

Table 5 shows the results of a random sample of patients with pain from musculoskeletal injuries treated with Acetaminophen, Ibuprofen, or Codeine. At =0.05can you conclude that the treatment is related to the result?

Result	Treatment
Acetaminophen	Ibuprofen	Codeine
Significant improvement	285	321	263
Slight improvement	169	237	158

Problem 6

Table 6 shows the results of a random sample showing vehicle types and and the types of crashes. At =0.025can you conclude that the type of vehicle is independent of the type of crash?

TypeofCrash	Vehicle
Car	Pickup	SUV
SingleVehicle	364	253	389
MultipleVehicle	289	165	351

Problems 7 and 8

Test the claim about the difference between two population variances, 12 and 22at the level of significance . Assume the samples are random and independent, and the populations are normally distributed.

Problem 7

7. Claim: 12=22, =0.05Sample statistics:12=283, 1=31,22=133,2=41

Problem 8

Claim: 1222, =0.05Sample statistics:12=463, 1=25,22=268,2=23

Problem 9

Golf balls. Company A claims the variance in the size of their golf balls is at most the variance in the size of the golf balls made by manufacturer B. A sample of 31 golf balls made by manufacturer A has a variance of 504 and a sample of 28 golf balls made by manufacturer B has a variance of 262. Assume the samples are random and independent, and the populations are normally distributed. At =0.05, can you reject manufacturer A's claim?

Section 10.4Problems 10 and 11

One-way ANOVA. Complete the hypothesis test and a one-way analysis of variance for each problem. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.

Problem 10

Gasoline prices. The Table 7 shows the gasoline prices (in dollars) for a sample of service stations. The prices are classified by vendor. At =0.05, is there enough evidence to conclude that at least 1 population mean gasoline price is different from the others?

Stewarts	7-Eleven	Fastrac
3.82	3.83	3.84
3.81	3.80	3.79
3.79	3.82	3.80
3.80	3.79	3.80
3.78	3.81	3.77
3.79		3.80

Problem 11

Student heights. Table 8 shows the heights (in inches) for a sample of students. The heights are classified by school. At =0.05, can you reject the claim that the population mean heights for all the schools is the same?

SchoolA	SchoolB	SchoolC
63.6	61.3	67.2
65.0	63.8	64.0
63.3	64.0	64.8
65.9	63.5	65.0
65.1	65.8	65.2
65.1	62.7	66.3

Problem 12

Two-way ANOVA. For this problem you must do a hypothesis test and a two-way analysis of variance. You must use one of the ANOVA: Two factor tools in the Data Analysis add-in Microsoft Excel and you must include the table produced by Excel with your work. Microsoft Excel uses the term replication for these tools and you must select the appropriate tool. When data are arranged in a table with one factor for the rows and the other factor for the columns, there is replication if there is more than 1 data entry at the intersection of each row and column. If there is only one data value at the intersection of each row and column, there is no replication.

Student test scores. Five students were randomly selected and their test scores in three subjects were recorded in Table 9. Assume the samples were gathered from normal populations, they are independent, and the populations have the same variance. At =0.05, can we conclude that the test scores are affected by either the students or the subject?

Student	Test Scores
Math	English	Science
a	79	78	86
b	81	86	84
c	82	91	81
d	73	79	76
e	78	81	75