state hypothesis and null hypothesis

Question

you are testing the claim of "the big cookie" company that it puts 20 chocolate chips in its big cookies. Many consumers have complained that they have been short changed. Test the claim from the consumers point of view. You select 49 cookies from different stores at different locations and find a mean of 17 chips with a standard deviation of 1. Test the claim at the 5% level of significance. State the hypothesis and do the drawing with the rejection region and correct t or z score. Compute the appropriate test statistic and make a decision as to the null hypothesis. If you reject the null hypothesis, make an observation to your findings.

Answer 1

First, you would state the null hypothesis

 

mean = 20

 

Second, the alternative hypothesis

 

mean < 20

 

Set up a normal distribution with mean of 17 and standard deviation of 1 with a z-score of 1.96 (5% level of significance).  The rejection region would be anything less than 1.96.

 

The z-score for the 49 bags would be (20-17)/1 = 3 which would be more than 1.96.  Because 3 > 1.96 it is not in the rejection region and therefore you fail to reject the null hypothesis.  Remember that you never accept the null hypothesis, but can only reject or fail to reject.