Question

Breyers is a major producer of ice cream and would like to test the hypothesis that the average American consumes more than 17 ounces if ice cream per month. A random sample of 15 Americans was found to consume an average of 18.2 ounces of ice cream last month. The standard deviation for this sample was 3.9 ounces. Breyers would like to set α = 0.10. The critical sample mean for this hypothesis test would be

Options:

	17.07
	17.46
	17.90
	18.35

Answer 1

Solution:

n= 15 sample size

$\mu=17\ ounces$. Population mean

. Sample mean

T = 18.2 ounces

s = 3.9 ounces sample standard deviations

level of significance.

a = 0.10

To test the hypothesis

$Ho:\mu=17$. Vs.   $Ha:\mu>17$

We can use t score to calculate the critical value for sample mean for a given sample size n= 15

$t= \frac{\bar X-\mu}{s/\sqrt n}$

$\bar X = t*\frac{s}{\sqrt n}+\mu$

Where  $t= t_{\alpha,n-1}=t_{0.10,14}=1.345$. From t table

$\bar X=1.345*\frac{3.9}{\sqrt 15}+17$

$\bar X=1.345*\frac{3.9}{3.8729833}+17$

$\bar X=1.345*1.0069756+17$

$\bar X=1.3543822+17$

$\bar X=18.354382$

$\bar X=18.35$

Critical sample mean is 18.35

Option D is correct.