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 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. Complete parts (a) through (d) below. a. Is there evidence that the mean amount is different from 1.0 gallon? (Use a=0.01.) Let u be the population mean. Determine the null hypothesis, Hg, and the alternative hypothesis, H. Họ P What is the test statistic? ZSTAT =O (Round to two decimal places as needed.) What islare the critical value(s)? (Use a=0.01.) (Round to two decimal places as needed. Use a comma to separate answers as needed.) What is the final conclusion? OA Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon. O B. Reject Ho There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon. OC. Fail to reject Ho. There is not sufficient evidence that the mean amount is different from 1.0 gallon. OD. Reject Ho There is not sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon. b. Compute the p-value and interpret meaning What is the p-value?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![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 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. Complete parts (a) through (d) below.
a. Is there evidence that the mean amount is different from 1.0 gallon? (Use a = 0.01.)
Let u be the population mean. Determine the null hypothesis, Ho, and the alternative hypothesis, H,.
Ho: H
H: p V1
What is the test statistic?
ZSTAT = (Round to two decimal places as needed.)
What is/are the critical value(s)? (Use a = 0.01.)
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
What is the final conclusion?
O A. Fail to reject Hn. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.
O B. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.
OC. Fail to reject Hn. There is not sufficient evidence that the mean amount is different from 1.0 gallon.
O D. Reject Ho. There is not sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.
b. Compute the p-value and interpret its meaning.
What is the p-value?
(Round to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafc75c11-f74c-4700-aac3-dcc346278078%2F97543bc9-4496-4fae-861b-41dafeef28e4%2F7otq82m_processed.png&w=3840&q=75)
![Interpret the meaning of the p-value. Choose the correct answer below.
O A. Fail to reject H,. There is not sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.
O B. Reject Ho. There is not sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.
O C. Fail to reject H,. There is sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.
O D. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.
c. Construct a 99% confidence interval estimate of the population mean amount of water per 1-gallon bottle.
sus (Round to four decimal places as needed.)
d. Compare the results of (a) and (c). What conclusions do you reach?
O A. The results of (a) and (c) are not the same.
O B. The results of (a) and (c) are the same.
OC. No meaningful conclusions can be reached.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafc75c11-f74c-4700-aac3-dcc346278078%2F97543bc9-4496-4fae-861b-41dafeef28e4%2Fqipclan_processed.png&w=3840&q=75)
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