QNT561 QNT/561 Week 4 Problem Set - 24547

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Try to exit and come back to the test until you get the same version.

1.      Which hypothesis, the null or the alternative, is the status-quo hypothesis?

2. What is the level of significance of a test of hypothesis?

3. For each of the following rejection periods, sketch the sampling distribution for z and indicate the location of the rejection region, and determine the probability that a Type I error will be made. a. z1.96; b. z1.645; d. z<-2.575.

4. A survey found that 85% of college presidents believe that their online education courses are as good as or superior to courses that use traditional face-to-face instruction. a. Give the null hypothesis for testing the claim made by the survey; b. Give the rejection region for a two-tailed test conducted at a = 0.01.

5. Several years ago, a government agency reported the default rate on a certain type of loan at 0.025. Set up the null and alternative hypotheses to determine if the default rate this year is greater than 0.025. 

6. For the a and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected. a=0.01 and p-value=0.10.

7. A study analyzes recent incidents involving terrorist attacks. 

2

3

1

2

2

1

1

2

2

4

1

1

5

1

1

1

1

4

1

2

a. Do the data indicate that the true mean number of suicide bombings of all terrorist group attacks against this country differs from 1.5? Use a=0.01 and p=0.1661.

b. A 99% confidence interval for the mean for the population was found to be 1.90 +-0.774. 

c. Do the inferences derived from part a and part b agree?

d. What assumptions about the data must be true for the inferences to be valid?

e. Use a graph to check whether the assumptions part d are reasonably satisfied.

8. When planning for a new forest road to be used for tree harvesting , planners must select the location to minimize tractor skidding distance. The skidding distances in meters were measured at 20 randomly selcted road sites. A logger working on the road claims the mean skidding distance is at least 421 meters. Is there sufficient evidence to refuse this claim? use a=0.10

444
576
410
549
286
432
486
345
460
198
387
291
184
263
270
405
310
307
135
422

9. Suppose 56 of 116 randomly selected shoppers believe that "Made in USA" means that 100% of labor and materials are from the United States. Let p represent the true proportion of consumers who believe that "Made in USA" means 100% of labor and materials are from the United States. 

10. A business journal investigation of the performance and timing of corporate acqusitions discovered that in a random sample of 2,983 firms, 702 announced one or more acqusitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acqusitions during 2000 is less than 26%? Use a=0.01.

11. Independent random samples from approximately normal populations produced the results shown below. 

Sample 1 Sample 2
44 60
26 51
31 51
35 50
49 54
42 27
20 35
37 33
60 50
57 66

a. Do the data present sufficient evidence to conclude that mean 1 - mean 2 is not equal 0? Use a=0.01.

b. Construct a 99% confidence interval for mean 1 - mean 2. 

12. A study was done to determine the effect of rudeness on a victim's task performance...The number of different uses for a brick was recorded for each of the 60 students 

Control Group Rudeness Condition
5 15
2 2
27 9
11 20
9 5
12 6
14 11
13 12
27 21
26 11
27 13
23 23
13 17
19 2
28 6
28 7
25 5
18 9
29 3
20 12
29 11
3 19
28 2
28 12
5 4
4 13
13 6
23 5
21 13
12 6

Conduct a statistical analysis (a=0.10) to determine if the true mean performance level for students in the rudeness condition is lower than the true mean performance level for students in the control group.

13. The data for a random sample of six paired observations are shown in the table:

Pair Population 1 Sample (Observation 1) Population 2 Sample (Observation 2)
1 3 1
2 3 2
3 3 3
4 2 3
5 8 5
6 5 4

a. Calculate d and s^2.

b. Form a 99% confidence interval.

c. Test the null hypothesis: mean=0 against alternative hypothesis mean not equal 0. Use a=0.01. 

14. The data for a random sample of 8 paired observations are shown in the table:

Pair Population 1 Population 2
1 28 29
2 52 59
3 33 36
4 21 24
5 15 17
6 45 46
7 41 44
8 28 31

a. What are the appropriate null and laternative hypotheses to test whether the mean for population 2 is larger than the population 1?

b. Conduct the test identified in part a using a=0.05.

c. Find a 95% confidence interval.

d. What assumptions are necessary to ensure the validity of this analysis?

15. Construct a 95% interval for (p1 - p2)in each of the following situations:

a. n1=400, p1=0.63, n2=400, p2=0.57.

b. n1=180, p1=0.33, n2=250, p2=0.24.

c. n1=100, p1=0.46, n2=120, p2=0.59.

16. A newspaper reported the results of a survey on the planning habits of men and women . In response to a question “What is your preferred method of keeping track of meetings?” 54 of men and 44 of women answered “I keep them in my head”. A nationally representative sample of 1,000 adults participated in the survey; therefore, assume that 500 were men and 500 were women.

a. a.Set up the null and alternative hypotheses for testing whether the percentage of men who prefer keeping track of appointments in their head, p1, is larger than the corresponding percentage of women, p2
b. Compute the test statistic for the test.

c. Give the rejection region for the test, using a=0.01.

d.Find the p-value for the test.

e. Make an appropriate conclusion.

 

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