STAT244 LS PracticeQuiz #4

1. A survey of why people lost their jobs produced the following results. At α=.05, test the claim that the number of responses is equally distributed. Use the p-value method.

Reason / Company closing / Position abolished / Insufficient work
Number / 26 / 18 / 28

a) What are the null and alternative hypotheses?

H0:

H1:

b) Compute expected counts.

Reason / Company closing / Position abolished / Insufficient work
Expected Number

c) What are the required counts for the Chi-square test? Are those counts satisfied?

d) Compute the test statistic, degrees of freedom, and P-value.

Reason / Company closing / Position abolished / Insufficient work
Number / 26 (24) / 18 (24) / 28 (24)

d. f. =

from Table D.

e) Make a conclusion.

2. A pizza shop owner wishes to determine if the type of pizza a person selects is related to the age of the individual. The data obtained from a sample are shown. At α = .01, is the age of the purchaser related to the type of pizza ordered? Use the p-value method.

Age / Plain / Pepperoni / Mushroom / Double cheese / Row total
10 - 19 / 12 / 21 / 39 / 71 / 143
20 - 29 / 18 / 76 / 52 / 87 / 233
30 - 39 / 24 / 50 / 40 / 47 / 161
40 - 49 / 52 / 30 / 12 / 28 / 122
Col total / 106 / 177 / 143 / 233 / 659

a) What are the null and alternative hypotheses?

H0:

H1:

b) Compute expected counts.

Age / Plain / Pepperoni / Mushroom / Double cheese
10 - 19 / 23.00
20 - 29 / 37.48 / 62.58
30 - 39 / 25.90 / 43.24
40 - 49 / 19.62 / 32.77 / 26.47

e.g.) 143*106/659 = 23.00

c) What are the required counts for the Chi-square test? Are those counts satisfied?

d) Compute the test statistic, degrees of freedom, and P-value.

Age / Plain / Pepperoni / Mushroom / Double cheese
10 - 19 / 12 (23.00) / 21 (38.41) / 39 (31.03) / 71 (50.56)
20 - 29 / 18 (37.48) / 76 (62.58) / 52 (50.56) / 87 (82.38)
30 - 39 / 24 (25.90) / 50 (43.24) / 40 (34.94) / 47 (56.92)
40 - 49 / 52 (19.62) / 30 (32.77) / 12 (26.47) / 28 (43.14)

d. f. =

from Table D.

e) Make a conclusion.