Question

You would like see whether the number of chocolate chips is consistent with the picture on the bag of cookies. It appears from the picture on the bag that there should be about 5 chips per cookie. We would like to know if this is a reasonable conclusion, or not, given a sample of cookies (two- sided test). Since we don’t have any experience with cookie chip distributions, we are going to conduct a nonparametric test to see if our assumption of five chips is correct. The number of chips found in eight cookies chosen at random was: 4 7 3 8 7 6 5 9

a. State the appropriate null and alternative hypotheses for this question.

b.Determine the appropriate rejection region for a Type I error of 5%.

c.Calculate the appropriate test statistic and test the null hypothesis. Show your work. State your conclusion.

Answer 1

(a) H0: Null Hypothesis: 5 chips per cookie

    HA: Alternative Hypothesis: Not 5 chips per cookie

(b) = 0.05

ndf = n - 1 = 8 - 1 = 7

From Table, critical value of = 14.0671

Rejection region:
Reject H0 if calculated value of > 14.0671

(c)

O                   (O - E)²/E

4                       0.2

7                      0.8

3                    0.8

8                   1.8

7                    0.8

6                  0.2

5                    0

9                  3.2

-----------------------

        = 7.8

Since the calculated value of = 7.8 is less than critical value of = 14.0671, Fail to reject H0.

Conclusion:

The data support the claim that there are about 5 chips per cookie.