Question

The following case is for Questions 16-18:

The General Social Survey has a survey question: “Would you be willing to pay much higher taxes in order to protect the environment?” To test whether there is a difference between this year’s “Yes” rate and last year’s “Yes” rate, a sample of 500 people this year (Group 1) and 500 people last year (Group 2) were selected. Results show that 245 people said “Yes” this year and 225 people said “Yes” last year.

Assume α=0.05.

Question 16:

What is the test statistic?

(a) 0.04

(b) 1.27

(c) 0.06

(d) 2.54

Question 17:

What is the 95% confidence interval for the difference in “Yes” rate between this year and last year?

(a) (0.49-1.96*0.022, 0.49+1.96*0.022)

(b) (0.49-1.65*0.022, 0.49+1.65*0.022)

(c) (0.04-1.96*0.03, 0.04+1.96*0.03)

(d) (0.04-1.65*0.03, 0.04+1.65*0.03)

Question 18:

What is the rejection region?

(a) z<-1.96 or z>1.96

(b) z<-1.645 or z>1.646

(c) z>1.645

(d) z<-1.645

Answer 1

16)

The null and alternate hypothesis are:

The test statistic value is given by:

Hence option B is the correct option.

17)

We know that the 95% confidence interval for difference of proportions is given by:

Hence option C is the correct option.

18)

Since this is a two-tailed test, so the critical values are:

and

So, the rejection region is: z<-1.96 or z>1.96

Hence option A is the correct option.