Question

A researcher is looking into whether who wear Crocs sandals are less cool than people who wear other sandals. He knows that the mean “coolness” score for people who wear other sandals is 21, with a population standard deviation of 6. He takes a sample of 9 people who wear Crocs and finds a sample mean coolness score of 17.4. Should the researcher reject the null hypothesis in this study? Assume alpha = .05.

a. No, they should not reject the null hypothesis because the p-value is less than the z-score

b. Yes, they should reject the null hypothesis because the z-score is less than the p-value

c. Yes, they should reject the null hypothesis because the p-value is less than alpha

d. No, they should not reject the null hypothesis because the p-value is not less than alpha

Answer 1

Solution :

1) The null and alternative hypothesis are,

H0 : = 21 ......... Null hypothesis

Ha :   < 21 ......... Alternative hypothesis

Here , n = 9 , = 17.4 , = 6

2)The test statistic t is

z = [ - ]/ [ /9] = [17.4 - 21]/[6 /9] = -1.8

The value of the test​ statistic z = -1.8

3) Now ,

sign in Ha indicates that the test is ONE TAILED.

z = -1.8

So , using calculator ,

p value = p( z < -1.8 )

   = 0.0359

4) p value is less than the significance level 0.05.

Decision: Reject the null hypothesis H0

Answer : Option C is correct.

Yes, they should reject the null hypothesis because the p-value is less than alpha.