Question

(a) Write the claim mathematically and identify H, and H, (b) Find the critical value(s) and identify the rejection region(s) (c) Find the standardized test statistic (d) Decide whether to reject or fail to reject the null hypothesis An environmental agency recently claimed more than 27% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1000 consumers, you find 36% have stopped buying the product. At = 0.03, do you have enough evidence to support the claim? (a) Which of the following correctly states H, and H,? O A. Ho p=0.27 HA 70.27 OD. He: p=0.27 Hp>0.27 OB. Ho:p>0.27 Hp0.27 OE H, P20:27 Hp<0.27 OC. Họ p < 0.27 Hyp>0.27 OF H, p<027 Hp20.27 (b) What is (are) the critical value(s) Zo? 20 (Use a comma to separate answers as needed. Round to two decimal places as needed) Which of the following graphs has the rejection region(s) shaded correctly?

Answer 1

Solution:

Null hypothesis H0: mean <=0.27

Alternate hypothesis Ha: mea> 0.27

So its correct answer is C.

At alpha = 0.03, Z critical value = 2.75

If test stat value is greater than 2.75 then reject the null hypothesis as do not reject the null hypothesis.

Its correct shades region is A.

Zstat = (0.36-0.27)/sqrt(0.27*0.73/1000) = 0.09/0.0140 = 6.43

As we can see that z stat value is greater than z crit value so we can easily reject the null hypothesis and we have significant evidence to support the alternative hypothesis

So its answer is A. I.e. reject the null hypothesis. There is enough evidence to support the claim.