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BUS4025 – Assignment 7
For these problems, please use Excel to show your work, and submit the Excel spreadsheet along with your completed assignment.
1. For the following problems, state the null and alternate hypothesis, find the chi-square test statistic, decide whether to reject or fail to reject the null hypothesis, and provide your analysis and conclusions.
a. Results from a survey five years ago that asked how long they had to wait in the waiting room to see their doctor. You randomly selected 250 people and asked them how long they had to wait in the waiting room. Can you conclude at sig. of .01 that there has been a change in claimed or expected distribution?
Actual Minutes
Actual Percentage
Survey Result Minutes
Survey Result Frequency
1 – 5
14%
1 – 5
21
6 – 10
18%
6 – 10
39
11 – 15
27%
11 – 15
37
16 – 20
15%
16 – 20
53
21 – 25
11%
21 – 25
40
26 – 30
9%
26 – 30
34
31 and over
6%
31 and over
26
b. Results from a previous survey asked baseball players on a high school team what they needed help with the most in baseball. To determine whether the distribution is the same, a researcher studied 125 randomly selected players and asked them what they needed the most help with. The results are shown below. At a sig. of .05 are the distributions the same?
Actual Percentage
Survey Result
Bunting
11%
18
Batting Approach
38%
33
Strategy
26%
47
Throwing Velocity
25%
27
2. For the following problems, find the expected frequencies of each cell in the table, perform a chi-square test for independence, and comment on the relationship between the variables. Assume the variables are independent.
a. The contingency table shows the results of a random sample of college professors and the years of teaching at the university level.
Gender
< 1 Year 1 – 3 Years 4 – 7 Years 8 – 15 Years Over 15 Years Male 35 47 58 135 150 Female 53 68 128 97 54
b. The contingency table shows the results of a random sample of individuals by gender and gas mileage of vehicle owned.
Gender
1 – 15 MPG
16 – 21 MPG
22 – 28 MPG
29 – 35 MPG
Over 35 MPG
Male
13
86
118
87
24
Female
11
45
68
134
128
3. The table below shows the raw score for reading comprehension on a college entrance exam for 7 randomly selected male students and 10 randomly selected female students. Assuming that the entrance exam test scores are normally distributed, at a sig. of .05, test the claim that the test score variance for females is different from the males.
Female
47
48
53
41
38
56
58
36
40
47
Male
48
49
47
60
57
58
52
4. In the following problems, use the given sample data to perform a one-way ANOVA test using a .05 level of significance. What are your conclusions? Assume the sample is drawn from a normal population, the samples are independent, and the populations have the same variances
a. The table shows the average annual cost of high speed internet access in dollars for a random sample of individuals in four different regions of a state.
Northern
Southern
Eastern
Western
125
145
162
171
130
120
158
168
115
140
145
187
124
138
143
155
120
162
168
b. The table shows the annual income for a random sample of individuals in four regions of a state.
Northern
Southern
Eastern
Western
34,000
38,000
54,000
110,000
48,000
49,000
65,000
89,000
57,500
60,750
78,000
65,000
42,000
51,500
62,000
128,000
62,500
55,500
38,500
5. Application: Create a data set of your own regarding something of interest to you. Populate the data set with sample data (at least 10 records). Use your sample data set to perform a one-way ANOVA test using a .05 level of significance. What are your conclusions? Assume the sample is drawn from a normal population, the samples are independent, and the populations have the same variances.
6. For the following problems, identify the claim and state the null and alternate hypotheses, determine the critical value, find the test statistic, determine whether to reject or fail to reject the null hypothesis, and interpret the decision in the context of the original claim.
a. The store manager claims that the median number of customers per day through the checkout lines is no more than 225. A sample of customers per day through the checkout lines over 15 days is listed below. At .05 can you reject the manager’s claim?
215 224 261 208 194 198 230 216
213 200 154 223 210 174 187
b. A loan officer at a bank maintains that the median credit rating of its customers pursuing a mortgage loan is at least 695. The credit scores for 20 randomly selected mortgage loan customers is listed below. At .05 can you reject the loan officer’s claim?
617 695 706 631 711 625 653 612 707
719 605 619 621 699 644 665 697 609
687 711
c. A local police agency states that the median ticket cost for a speeding ticket issued is $185. In a random sample of 35 speeding tickets, the data is below. Can you reject the claim that the median ticket cost for a speeding ticket is $185?
154 158 135 157 185 100 178 140 177 97 111 99 115 156 147 102 140 175 185 114 142 128 224 159 131 187 167 145 120 218 195 201 130 194 221
7. For the following, determine whether the samples are dependent or independent, and choose the appropriate Wilcoxon test, state the null and alternate hypothesis, determine the critical values, find the test statistic, state whether you reject or fail to reject the null hypothesis, and explain your answer.
a. A college estimates the number of semesters it takes to complete a bachelor’s degree differs by gender. The table shows 10 male and 10 female students (randomly selected) and the number of semesters to complete the degree.
Male
18
17
15
20
16
20
18
16
17
19
Female
16
17
17
16
18
20
21
18
19
16
8. For the following use the Spearman rank correlation coefficient to test the claim. Identify and state the null and alternate hypothesis, find the test statistic, decide whether to reject the null hypothesis, and form an analysis of your findings.
a. Overall scores and the prices for 10 randomly selected flat screen televisions. The score is based on overall quality of the television. At a .05 sig. can you conclude there is a correlation between price and score?
Score
91
94
99
89
86
81
72
85
94
98
86
Price (in dollars)
1250
1500
1495
1150
1195
1685
989
1175
1350
1425
1300
