King Abdul Aziz University Department of Statistics
Assignment 5(Chapters 11 and 12) Stat 271
Term 2, 2014
Name:______________________________
ID:_________________________________
Section:_____________________________
Marks Obtained:______________________
Please mark all your answers on the answer sheet
The due date Sunday & Monday 13 and 14/6/1435
1
1. Which of the following is not an assumption of the independent t-test?
A) Normality B) Independence C) Equal sample sizes D) None of the above
2. The paired difference test has ………. degrees of freedom A) ( )
B) C)
D) ( )
3. When testing for a difference between the means of two dependent samples
A)
B)
C)
D) Either B or C .
4. The F distribution is
A) continuous and negatively skewed B) continuous and positively skewed C) continuous and symmetric
D) discrete and negatively skewed
A number of minor automobile accidents occur at various high-risk intersections despite traffic lights. The traffic Department claims that a modification in the type of light will reduce these accidents. Eight intersections were chosen at random, and the lights at those intersections were modified. The numbers of minor accidents during an eight-month period before and after the modifications were:
Number of accidents Before
modification
After modification
5 3
7 7
6 7
4 0
8 4
9 6
8 8
10 2
At the 0.01 significance level, is it reasonable to conclude that the modification reduced the number of traffic accidents?
2
Answer the questions 5-10 5. The null hypothesis and alternate hypothesis are:
A) : vs. : B) : vs. : C) : vs. : D) : vs. :
6. The p-value(s) for checking normality is (are):
A) 1.0000 B) 0.3173 C) 0.1573 D) A and B
7. The test statistics value of the test is:
A) 2.42 B) 2.50 C) 0.124 D) 3.411
8. The p-value for the hypothesis test is:
A) 0.9768 B) 0.0039 C) 0.0232 D) 0.0079
9. The tabulated critical value(s) of test is (are):
A) -2.998 B) 2.998 C) 2.33 D) -2.33
10. The decision and conclusion of testing this claim is:
A) Reject H0, there is enough evidence to support the claim B) Not reject H0, there is enough evidence to reject the claim C) Reject H0, there is enough evidence to reject the claim
D) Not reject H0, there is not enough evidence to support the claim
3
A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers (R) is more than that of decaffeinated-coffee drinkers (D). The standard deviation for those drinking regular coffee is 1.20 cups per day and 1.36 cups per day for those drinking decaffeinated coffee. A random sample of 20 regular-coffee drinkers showed a mean of 4.5 cups per day. A sample of 25 decaffeinated-coffee drinkers showed a mean of 5.35 cups per day.
Assume that both samples are normally distributed and use the 0.05 significance level to test if the mean daily consumption of regular-coffee drinkers (R) is more than that of decaffeinated- coffee drinkers (D).
Answer the questions 11-14 11. The null hypothesis and alternate hypothesis are:
A) : vs. : B) : vs. : C) : vs. : D) : vs. :
12. The test statistics value of the test is:
A) 1.73 B) 2.22 C) 3.05 D) -2.22
13. The tabulated critical value of test is : A) 1.64
B) 2.416 C) -1.64 D) -2.416
14. The decision and conclusion of testing this claim is:
A) Reject H0, the mean daily consumption of regular-coffee (R) drinkers is more than that of decaffeinated-coffee (D) drinkers
B) Reject H0, the mean daily consumption of regular-coffee (R) drinkers is less than that of decaffeinated-coffee (D) drinkers
C) Not reject H0, the mean daily consumption of regular-coffee (R) drinkers is less than or equal of decaffeinated-coffee (D) drinkers
D) Not reject H0, the mean daily consumption of regular-coffee (R) drinkers is greater than or equal of decaffeinated-coffee (D) drinkers
4
The following data resulted from a taste test of two different chocolate bars, which is a rating of the taste from 0 to 5, with a 5 indicating the person liked the taste.
Rating for chocolate bar (1)
Rating for chocolate bar (2)
3 1
1 4
4 2
2 1
1 1
0 3
2
At the 1% significance level, do these data show a difference in the taste ratings?
Answer the questions 15-20 15. The null hypothesis and alternate hypothesis of test are:
A) : vs. : B) : vs. : C) : vs. : D) : vs. :
16. The appropriate test is:
A) t-test (pooled variance) B) t-test (unequal variance) C) z-test
D) F-test
17. The pooled standard deviation is equal to:
A) 1.714 B) 0.728 C) 2.611 D) 1.309
18. The tabulated critical value(s) of test is (are):
A) ±3.106 B) 2.718 C) -2.718 D) ±3.169
5 19. The p-value of test:
A) 0.8481 B) 0.8477 C) 0.9120 D) 0.8612
20. The decision of test is:
A) Reject H0, there is a difference in the taste ratings between tow chocolate bars B) Reject H0, there is no difference in the taste ratings between tow chocolate bars C) Not reject H0, there is no difference in the taste ratings between tow chocolate
bars
D) Not reject H0, there is a difference in the taste ratings between tow chocolate bars
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A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to plan A is $44,000 with a standard deviation of $9,000, and a sample of 30 subscribers to plan B, the mean income is $50,000 with a standard deviation of $7,100.
Use the 0.1 significance level to test if the mean income of those selecting Plan B is larger.
Answer the questions 21-24
21. The null hypothesis and alternate hypothesis of test are (respectively):
A) : vs. : B) : vs. : C) : vs. : D) : 0 vs. :
22. The appropriate test statistic of the test is:
A) t for (pooled variance t-test) B) t for (unequal variance t-test) C) Z for (independent z-test) D) Z for (dependent z-test)
23. The value of the p-value of the test is:
A) 0.0009 B) 0.1871 C) 0.0018 D) 0.9892
6 24. The decision of test is:
A) Reject H0, mean income of plan A is less than mean income of plan B B) Reject H0, mean income of those selecting Plan B is not larger
C) Not reject H0, mean income of plan A is less than mean income of plan B D) Not reject H0, mean income of those selecting Plan B is larger
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A dairy company claims that its 120g low-fat yogurt cups contain fewer calories than the 120g low-fat yogurt cups produced by a competitor. A consumer agency wants to check this claim.
Then, a sample of 27 yogurt cups produced by this company (1) showed that they contain an average of 61 calories per cup with standard deviation 4.1 calories per cup. A sample of 22 yogurt cups produced by its competitor (2) showed that they contain an average of 70 calories per cup with standard deviation 1.9 calories per cup. Use the 0.05 significance level to test the dairy company’s claim. Assume that, low-fat yogurt calories for each company are normally distributed.
Answer the questions 25-28
25. The null hypothesis and alternate hypothesis of test are (respectively):
A) : vs. : B) : vs. : C) : vs. : D) : vs. :
26. The value of the p-value of the test is:
A) 0.1983 B) 0.0581 C) 1.14E-12 D) 0.0006
27. The tabulated critical value(s) of test is (are):
A) -1.678 B) 1.64 C) -1.686 D)
28. The decision of test is:
A) Reject H0, there is enough evidence to support the claim B) Reject H0, there is not enough evidence to reject the claim C) Not reject H0, there is not enough evidence to support the claim D) Not reject H0, there is enough evidence to support the claim
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7
In 2005, a sample of 300 households in Jeddah showed that 72 paid their monthly phone bill by debit card. In 2009, a sample of 400 households in the same city showed that 120 paid their monthly phone bill by debit card. Test whether the percentage of households paying their phone bill by debit card remained the same at α = 0.01.
Answer the questions 29-34 29. The null hypothesis and alternate hypothesis are:
A) : vs. : B) : vs. : C) : vs. : D) : vs. :
30. The value of the pooled proportion is:
A) 0.174 B) 0.24 C) 0.30 D) 0.274
31. The p-value of test is:
A) 0.0783 B) 1.47E-11 C) 3.62E-05 D) 0.0308
32. The critical value and test statistic are:
A) ±2.58 and z = -4.13 B) -2.33 and z = 3.24 C) ±2.58 and z = -1.76 D) 2.33 and t = -1.06
33. Choose the correct answer, based on test:
A) The confidence interval contains the value of proportions differences (zero) B) p-value > α.
C) The confidence interval not contain the value of proportions differences (zero) D) A and B
8 34. The decision of testing this claim is:
A) Not Reject H0, the percentage of households paying their phone bill by debit card is different between the two years
B) Not reject H0, the percentage of households paying their phone bill by debit card remained the same between two years.
C) Reject H0, the percentage of households paying their phone bill by debit card remained the same between two years
D) Reject H0, the percentage of households paying their phone bill by debit card is different between the two years
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35. . A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa and Discover. Six MasterCard sales, seven Visa and five Discover sales were recorded.
The store used an ANOVA to test if the mean sales for each credit card were equal.
What are the degrees of freedom for the F statistic?
A) 18 in the numerator, 3 in the denominator.
B) 3 in the numerator, 18 in the denominator. C) 2 in the numerator, 15 in the denominator.
D) 6 in the numerator, 15 in the denominator.
A consumer organization claims that there is a difference in the variation of the price of a particular toy at two different types of stores. The price of the toy was checked in a sample of 7 discount stores and 8 department stores. The results are shown below. Use the 10% significance level to test their claim.
Discount 12 13 14 12 15 15 17
Department 19 17 16 20 19 14 18 17
Answer the questions 36-39 36. The null hypothesis and alternate hypothesis are:
A) : vs. : B) : 0 vs. : C) : vs. :
D) : vs. :
37. The p-value of the test:
A) 0.0033 B) 0.9111 C) 0.0036 D) 0.0003
9 38. The critical value (s) is (are):
A) 4.21 B) 3.01 C) 10.70 D) ±1.771
39. The decision of testing this claim is:
A) Reject H0, the consumer organization claim is correct B) Not reject H0, the consumer organization claim is correct C) Reject H0, the consumer organization claim is not correct D) Not reject H0, the consumer organization claim is not correct
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The questions (40-45) are based on the Banking data set on the Data Sets folder
Is there a difference in the mean Balance among the number of Services? (test the mean balance in cases of the 3, 4, 5 and 6 services)? Use the .05 significance level.
40. State the null and alternative hypotheses.
A) : vs. : B) : vs. : C) : vs. :
D) : vs. : Treatment means are not all equal 41. The value of the grand mean is:
A) 6496.8 B) 515.92 C) 216.12 D) 1596.3
42. The value of the F tabulated is:
A) 2.85 B) 3.52 C) 2.87 D) 0.88
43. What are the total degrees of freedom:
A) 3 B) 35 C) 38 D) 39
10 44. What is the mean square for error:
A) 235,726.241 B) 9407402.7125 C) 268,782.935 D) 6324.7693
45. What is your decision:
A) Reject H0, there is a significant difference between treatment means B) Reject H0, the treatment means are all equal
C) Not reject H0, there is not significant difference between treatment means D) Not reject H0, the treatment means are not all equal
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11
The answer sheet:
D C
B A
23.
D C
B A
1.
D C
B A
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D C
B A
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D C
B A
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D C
B A
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D C
B A
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D C
B A
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D C
B A
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D C
B A
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B A
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B A
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B A
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B A
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B A
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B A
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B A
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B A
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B A
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