Question

melissa and madeline love pepperoni pizza, but sometimes they are disappointed with the small number of pepperonis on their pizza. to investigate, they went to their favorite pizza restaurant at 10 randomly selected times during the week and ordered a large pepperoni pizza. here are the number of pepperonis on each pizza.
47
36
25
37
46
36
49
32
32
34
according to the manager of the restaurant, there should be an average of 40 pepperonis on a large pizza. a 95% confidence interval for \\(\mu\\) = the true mean number of pepperonis on a large pizza at this restaurant was conducted. the interval was 31.919 to 42.881.
is there convincing evidence that the average number of pepperonis is less than 40? explain your reasoning.
because
, there
convincing
evidence that the average number of pepperonis is less than 40.

Explanation:

Step1: Analyze confidence interval

The 95% confidence interval for $\mu$ is $(31.919, 42.881)$.

Step2: Check value 40 in interval

The value 40 lies within $31.919 < 40 < 42.881$.

Step3: Interpret interval result

A confidence interval containing the claimed mean (40) means we cannot reject the claim that the true average is 40; there is no evidence it is less than 40.

Answer:

Because 40 is contained within the 95% confidence interval (31.919 to 42.881), there is no convincing evidence that the average number of pepperonis is less than 40.