Question

Toppings
Pepperoni	Canadian Bacon	Pineapple	Cheese	Mushrooms	Steak	Chicken	Sausage
13	3	2	2	1	1	1	1

The 95% confidence interval for the true proportion of pepperoni being the preferred topping is [1.3052,4.6947].

From the data above, the hypotheses H₀: µ <= .40 and H_A: µ > .40, and an alpha level of 0.1

Pepperoni is H₀: µ <= .40 and H_A: µ >.40 , testing if people actually get pepperoni more often than not

Answer 1

At 0.1 level of signficance, z critical value for right tailed hypothesis is 1.28 (using z distribution table)

Sample proportion p(hat)  = 13/24 = 0.542

population proportion po = 0.40 (given in question)

sample size is n = 24 (total number of toppings)

z test statistics calculation

To find the corresponding p value, check z distribution with 1.42 in column and 0.02 in row and then the intersecting cell will give us p value = 0.0778

p value is less than significance level of 0.10, rejecting the null hypothesis.

We can conclude that population proportion is higher than 0.40