Question

1. Suppose it is claimed that the mean weight of a bag of the same brand of candies is 0.13 ounces. You wish to show that it is not 0.13 ounces and wish to test the claim at α = 0.01 level. You collected a sample of 16 small bags of the same brand of candies. The weight of each bag was then recorded. The mean weight was two ounces with a standard deviation of 0.12 ounces. Assume that the population distribution of bag weights is normal with a known population standard deviation of 0.1 ounce.
   1. State the null and alternate hypotheses clearly.
   2. Conduct the hypothesis test based on the test statistic and critical value(s). Clearly indicate each.
   3. What is the p-value? Use the p-value to conduct the same test
   4. Report your conclusion in words, in the context of the problem.

Answer 1

Solution:

Given ,

= 0.13

claim :     0.13

n = 16

= 0.12

= 0.1

Use = 0.01

a) Hypothesis are

H0 : = 0.13 (null hypo.)

H1 :     0.13

b)The test statistic z is given by

z =

= (0.12 - 0.13) / (0.1/16)

= -0.40

Now , observe that ,there is   sign in H1. So , the test is two tailed.

So there are two critical values.   i.e.  

i.e.   2.576 (Use z table to find this value)

Critical values are -2.576 and 2.576

Since |z| = 0.40 is less than |2.576| , we fail to reject the null hypothesis.

c) For two tailed test :

p value = 2 * P(Z < -z)

= 2 * P(Z < -0.40)

= 2 * 0.3446

= 0.6892

Since the p value is greater than = 0.01 , we fail to reject the null hypothesis.

d)We fail to reject the null hypothesis.

We can conclude that the  mean weight of a bag of the same brand of candies is NOT DIFFERENT from 0.13