Question

Solve the following questions

9. Males and females were asked about what they would do if they received a $100 bill by

mail, addressed to their neighbor, but wrongly delivered to them. Would they return it to

their neighbor? Of the 100 males sampled, 85 said yes and of the 200 females sampled, 180

yes. Does the data indicate that the percentages that said yes is higher for female than for

male? We set the hypothesis as: H0 : p1 = p2, H1 : p1 < p2.

By the formula

Z = √ ˆpˆpn1 1ˆq1 1 − + ˆp2 ˆpn2

2ˆq2 ,

we find Z = −1.20. Then, the P-value is:

(A) 0.1936 (B) 0.0968 (C) 0.159706 (D) 0.1151 (E) 0.2302.

4

10. “Do you believe this policy is necessary? ” To get the answers from people, suppose you

did a survey and asked n = 120 people. They were asked to state their opinion on a 4 point

scale regarding the question. The following is your survey result.

Attitude Count Strongly Disagree 33 Disagree 30 Agree 25 Strongly Agree 32

a). The Chi-square value is:

(A) 1.27 (B) 1.45 (C) 1.68 (D) 1.93 (E) 2.10.

b). Your decision is:

(A). Since p-value > 0.10, we believe at α = 0.10 that there is no difference in the proportions

of people with different opinion.

(B). Since p-value < 0.10, we believe at α = 0.10 that there is difference in the proportions

of people with different opinion.

(C). Since p-value > 0.10, we believe at α = 0.10 that there is difference in the proportions

of people with different opinion.

(D). Since p-value < 0.05, we believe at α = 0.05 that there is difference in the proportions

of people with different opinion.

5

11. Last year, five randomly selected students took a math aptitude test before they began

their statistics course. Suppose we want to know that, based on math aptitude scores, what

linear regression equation best predicts statistics performance? The scores for those five

students are listed in the following table. In the table, the xi column shows scores on the

aptitude test, and the yi column shows statistics scores. We find ̄x = 78, and ̄y = 77. Based

on the table, we want to find the equation of the regression line y = a + bx.

Student xi yi (xi − ̄x) (yi − ̄y) 1 95 85 17 8 2 85 95 7 18 3 80 70 2 −7 4 70 65 −8 −12 5 60 70 −18 −7

a). We find the regression line is:

(A) y = 12.4+4.2x (B) y = 18.76 + 1.24x (C) y = 26.78 + 0.64x (D) y =

20.42 + 1.6x

b). From computer, we find SSR = 302, SSE = 327. The, the F-value is:

(A) 1.67 (B) 2.77 (C) 3.69 (D) 4.61

c). Your conclusion is:

(A). At α = 0.05, we believe that there is linear relationship between x and y.

(B). At α = 0.05, we believe that there is no linear relationship between x and y.

Answer 1