Question

Dr. Christina Cuttleman, a nutritionist, claims that the average number of calories in a serving of popcorn is 75 with a standard deviation of 7. A sample of 50 servings of popcorn yields an average of 78 calories.

A. Should z test or t test be used?
B. Check Dr. Cuttleman's claim at a = 0.05.

Answer 1

a) T test

b) Claim

because critical value is not equal to test statistic then reject null hypothesis

Explanation:

Construction of hypothesis

H₀ : p = 75

H₁ : p ≠ 75

Here Standard deviation = 7

sample = n = 50

Average = x-bar = 78

Level of significance:

∝ = 5% = 0.05

Degree of freedom:

df = n-1

= 50 -1 = 49

Critical value :

± 1.96

a) T test

test t is used as average X mean is used

Test Statistic:

t = X₂ - X₁ / Sd /√n

= 78 - 75 / 7/√50

=3.0304

Critical region :

We take two tail T test

test statistic is in reject interval. Reject H₀

b) Claim

because critical value is not equal to test statistic then reject null hypothesis