Question

A package of a certain type of cookies claims that there are about 11 grams of sugar in a single cookie. Evaluate the validity of this claim based on a sample of 14 randomly chosen cookies which had the mean value of 11.2g of sugar with standard deviation 0.3g. Use α = 0.05 significance level.

a. State the hypotheses and identify the claim.

b. Compute the test value.

c. Find the critical value.

d. Make the decision to reject or not reject the null hypothesis. Justify.

e. Summarize the results.

Answer 1

a)

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 11

Ha: 11

b)

The test statistics,

t =( - )/ (s /n)

= ( 11.2 - 11 ) / ( 0.3 / 14 )

= 2.494

c)

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.771

d)

Since it is observed that t = 2.494 > = 1.771, it is then concluded that the null hypothesis is rejected.

e)

There is sufficient evidence to claim that there are about 11 grams of sugar in a single cookie.