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
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