Question

A fast-food chain claims one large order of its fries weighs 170 grams. Joe thinks he is getting less than what the restaurant advertises. He weighs the next 12 random orders of fries before he eats them and finds the sample mean is 165.9 grams and the standard deviation is 11.98 grams. What conclusion can be drawn at α = 0.10?

There is not sufficient evidence to prove the fast-food chain advertisement is true.

There is sufficient evidence to prove the fast-food chain advertisement is false.

Joe has sufficient evidence to reject the fast-food chain's claim.

Joe does not have sufficient evidence to reject the fast-food chain's claim.

There is not sufficient data to reach any conclusion.

Answer 1

Here we are testing whether one large order of its fries weighs 170 grams, therefore the null and the alternate hypothesis here are given as:

The test statistic here is computed as:

For n - 1 = 11 degrees of freedom, we get from the t distribution tables that:

p = P(t₁₁ < -1.1855) = 0.1304

As the p-value here is 0.1304, which is higher than any significance level normally taken for a test, therefore the test is insignificant and we cannot reject the null hypothesis here. Therefore  Joe does not have sufficient evidence to reject the fast-food chain's claim.