Question

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.3 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 16.14 ounces. nbspTest whether the claim that the mean amount of juice for all 16 dash ounce bottles is less than 16.3 ounces is supported or not supported. Assume that sigma equals 0.9 ounces.

supported or not supported?

Answer 1

Step 1:

Ho: = 16.3

Ha: < 16.3

Null hypothesis states that the mean amount of juice is 16.3 ounce

Alternative hypothesis states that the mean amount of juice is less than 16.3 ounce

Step 2: Test statistics

n = 70

sample mean = 16.14

population sd = 0.9

z = -1.487

Step 3:

The z-critical value for a left-tailed test, for a significance level of α=0.05

zc = −1.64

As z stat (-1.487) does not fall in the rejection area, we fail to reject the Null hypothesis.
The claim is not supported. We donot have sufficient evidence to believe that the mean amount of juice is less than 16.3 ounce