Question

Please answer BOTH multiple part questions

2. You want to know about the country’s opinion of pizza.

2a. You take a random sample of 32 people and find that 13 of them like pizza. Find a point estimate for what proportion of the country likes pizza. Then, either find a 95% confidence interval for the proportion of the country that likes pizza, or explain why you can’t.

2b. Your random sample of 32 people has an average pizza consumption of 3.4 pizzas per year, with a standard deviation of 1.5 pizzas. Find a point estimate for the mean pizza consumption of the country. Then, either find a 95% confidence interval for the mean pizza consumption of the country, or explain why you can’t.

3. You want to know what your friends’ favorite Harry Potter movie is. There are eight movies in the series. You ask nine randomly chosen friends for their favorite Harry Potter movie and get the following answers: 1 2 3 3 3 4 6 8 8

3a. Find the mean, median, mode, and standard deviation of these numbers.

3b. For each of those statistics, explain whether it makes sense for this data set and why.

3c. What is it about this situation that makes these numbers statistics? What else would they be?

Answer 1

2a)

Answer)

N = 32

P = 13/32

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 13

N*(1-p) = 19

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table for 95% confidence level is 1.96.

Margin of error (MOE) = Z*√{P*(1-P)}/√N = 0.17016866058

Interval is given by

(P-moe, P+moe)

(0.23608133941, 0.57641866058)

2b)

As the population standard deviation is unknown here and we are using sample s.d as the best estimate, we will use t distribution table to construct the interval.

N = 32

Mean = 3.4

S.d = 1.5

Degrees of freedom is = n-1 = 31

For 31 dof and 95% confidence level, critical value t from t table is 2.04

Margin of error (MOE) = t*s.d/√n = 2.04*1.5/√32 = 0.541

Interval is given by

(Mean - MOE, Mean + MOE)

[2.859, 3.941].

You can be 95% confident that the population mean (μ) falls between 2.859 and 3.941.