Question

3. Pizza! A national pizza chain advertises that its large pizzas are 14 inches in diameter. The CEO wants to determine whether the average size of all of its pizzas adheres to that claim. She collects a random sample of 31 pizzas and measures each one. The sample results in an average diameter of 14.9 inches and a standard deviation of s = 2.10.

(a) Identify µ in this scenario. (Choose One) • Average diameter of all pizzas in the sample.

• 14 inches.

• True average diameter of all pizzas sold by the chain.

• We do not have enough information to answer this question.

(b) Conduct a hypothesis test for the above situation.

i. Identify the hypotheses H0 and Ha.

ii. Find the test statistic (Round your answer to 2 decimal places).

iii. Using the table below, select the most appropriate p-value.

P(T < t)--> 0.99

P(T > t) --> 0.01

P(T > |t|) --> 0.02

iv. Provide an interpretation of the p-value you chose from the table within the context of the problem by appropriately filling in the blanks: This p-value is the probability, assuming the is , of observing a test statistic at least as unusual as the one observed.

v. Based on the p-value, provide a conclusion in the context of the problem by appropriately filling in the blanks: There is evidence indicating that the is .

Answer 1

a) In this situation u= 14 inches.

b) We are testing,

I)H0: u= 14 vs H1: u not equal 14

II) Under H0, (sample mean- 14)/sample SD/√n ~ tn-1 distribution

So Test statistic: 14.9-14/(2.1/√31) = 2.386

iii) p- value of this two sided t- test: 2P(t30>2.386) = 0.0235 (from the t-tables)

So option c) is correct.

iv) So the probability of finding the u= 14 is as low as 0.02

v) Since the p-value of this test <0.05, we have sufficient to reject H0 and conclude that the u is not equal to 14.