Question

9.16 A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company is actually 1

gallon. You know from the water bottling company specifications that the standard deviation of the amount of water per bottle is 0.02 gallon. You select a random sample of 50 bottles, and

the mean amount of water per 1-gallon bottle is 0.995 gallon.

A) Is there evidence that the mean amount is different from 1.0 gallon? (Use α=0.01.)

B) Compute the p-value and interpret its meaning.

C) Construct a 99% confidence interval estimate of the population mean amount of water per bottle.

D) Compare the results of (a) and (c). What conclusions do you reach?

Answer 1

A) H₀: = 1.0

H₁: 1.0

The test statistic z = ()/()

= (0.995 - 1)/(0.02/)

= -1.77

At = 0.01, the critical values are +/- z_0.005 = +/- 2.58

Since the test statistic value is not less than the negative critical value(-1.77 > -2.58), so we should not reject the null hypothesis.

At = 0.01, there is not sufficient evidence to conclude that the mean amount is different from 1.0 gallon.

B) P-value = 2 * P(Z < -1.77)

= 2 * 0.0384 = 0.0768

C) At 99% confidence interval the critical value is z_0.005 = 2.58

The 99% confidence interval for population mean is

+/- z_0.005 *

= 0.995 +/- 2.58 * 0.02/

= 0.995 +/- 0.0073

= 0.9877, 1.0023

Since the confidence interval contains 1, so we should not reject the null hypothesis.

D) The results From (a) and (c) are same.

There is not sufficient evidence to conclude that the mean amount is different from 1.0 gallon.