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The manager of a paint supply store wants to determine whether the mean amount o

ID: 3131217 • Letter: T

Question

The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacture is actually 1 gallon. You know from the manufacturer's specifications that the standard deviation of the amount of paint is 0.02 gallon. You select a random sample of 55 cans, and the mean amount of paint per 1-gallon can is 0.995 gallon. Complete parts (a) through (d) below. Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. Is there evidence that the mean amount is different from 1.0 gallon? (Use alpha = 0.01.) Let mu be the population mean. Determine the null hypothesis, H_0, and the alternative hypothesis, H_1. What is the test statistic?

Explanation / Answer

Calculated z= -1.85

Critical values= (-2.58, 2.58)

Z Test of Hypothesis for the Mean

Data

Null Hypothesis                       m=

1

Level of Significance

0.01

Population Standard Deviation

0.02

Sample Size

55

Sample Mean

0.995

Intermediate Calculations

Standard Error of the Mean

0.0027

Z Test Statistic

-1.85

Two-Tail Test

Lower Critical Value

-2.58

Upper Critical Value

2.58

p-Value

0.0637

Do not reject the null hypothesis

Z Test of Hypothesis for the Mean

Data

Null Hypothesis                       m=

1

Level of Significance

0.01

Population Standard Deviation

0.02

Sample Size

55

Sample Mean

0.995

Intermediate Calculations

Standard Error of the Mean

0.0027

Z Test Statistic

-1.85

Two-Tail Test

Lower Critical Value

-2.58

Upper Critical Value

2.58

p-Value

0.0637

Do not reject the null hypothesis