Question

1. Create a 99% confidence interval for the proportion of cereals that have 100 CALORIES or less per serving based on the samples provided.

Calories
70
120
70
50
110
110
110
130
90
90
120
110
120
110
110
110
100
110
110
110
100
110
100
100
110
110
100
120
120
120
110
110
140
110
160
140
130
120
50
50

Answer 1

We sort the data from lowest to highest

The number of samples having 100 calories or less per serving = 12

Total number of samples = 40

Proportion of cereals that have 100 CALORIES or less per serving = 12/40 = 0.3

Given
p̂ = 0.3           ....... Sample Proportion
n = 40           ....... Sample Size

For 99% Confidence interval

α = 0.01,      α/2 = 0.005
From z tables of Excel function NORM.S.INV(α/2) we find the z value
z = NORM.S.INV(0.005) = 2.576
We take the positive value of z

Confidence interval is given by

= (0.1134, 0.4866)

99% Confidence interval for true proportion of cereals that have 100 CALORIES or less per serving is        calories

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