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 random times during the week and ordered a large pepperoni pizza. Here are the numbers of pepperoni on each pizza.
47 36 25 37 46 36 49 32 32 34
Use the 4 step method to construct and interpret a 95% confidence interval for the true mean number of pepperonis on a large pizza at this restaurant.

Using the t-distribution, it is found that the 95% confidence interval for the true mean number of pepperonis on a large pizza at this restaurant is (31.92, 42.88). It means that we are 95% that the true mean number of pepperonis for all large pizzas at the restaurant is within this interval.

In this problem, we will find the standard deviation for the sample, hence the t-distribution will be used.

What is a t-distribution confidence interval?

The confidence interval is given by:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.

t is the critical value.

n is the sample size.

s is the standard deviation for the sample.

For this problem:

The sample size is n = 10.

Using a calculator, we have that [tex]\overline{x} = 37.4, s = 7.66[/tex].

The critical value, considering a 95% confidence interval with 10 - 1 = 9 df, is of t = 2.2622.

The lower bound of the interval is:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 37.4 - 2.2622\frac{7.66}{\sqrt{10}} = 31.92[/tex]

The upper bound of the interval is:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 37.4 + 2.2622\frac{7.66}{\sqrt{10}} = 42.88[/tex]

The 95% confidence interval for the true mean number of pepperonis on a large pizza at this restaurant is (31.92, 42.88). It means that we are 95% that the true mean number of pepperonis for all large pizzas at the restaurant is within this interval.

More can be learned about the t-distribution at https://brainly.com/question/16162795