Your quality control manager wants to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours. Use pwzmean and pwciesigmaknown to help you.

1. At the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?

a. State the null and alternative hypothesis

b. State the decision rule

c. Compute the Z-statistic

d. State the decision

2. Compute the p-value and interpret its meaning.

3. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.

4. Based on your findings, what conclusions do you reach? How is the data useful for effective decision-making?

SIGMA Known:

Estimate for the Mean Paper Length 8480 Population Standard Deviation 0.02 Sample Mean 10.998 Sample Size 100 Confidence Level 9519 Intermediate Calculations Standard Error of the Mean 0.002 z value -1.9800 Interval Half Width 0.0039 Confidence interval Interval Lower Limit 10.9941 Interval Upper Limit 11.0019Estimate for the Mean Paper Length Data Population star 0.02 Sample Mean 10.998 Sample Size 100 Confidence Lev Intermediate Calculations Standard Error 0.002 anJEA Z -1.9600 Interval Half W 0.0039 Confidence Interval Interval Lower 10.9941 Interval Upper 11.0019Z Test for the Mean 2180 Null Hypothesis 368 Level of Significance 0105 Population Standard Deviation 15 Sample Size 25 Sample Mean 372 5 Intermediate Calculations Standard Error of the Mean 2 Test Statistic 15 Two-Tail Test Lower Critical Value -1 9800 Upper Critical Value 1.9600 Do not reject the null hypothesisCOMPUTE LOWER Z Test for the Mean Data Null Hypothesis 368 Level of Significance OTOS Population Standard Deviation 15 Sample Size 25 Sample Mean 372 5 Intermediate calculations Standard Error of the Mean 3 z Test Statistic 1.5 Lower-Tail Test Lower Critical Value -1 6449 p-Value 0.9332 Do not reject the null hypothesisCOMPUTE_UPPER Z Test for the Mean Data Null Hypothesis 388 Level of Significance OTOS Population Standard Deviation 15 Sample Size 25 Sample Mean 372 5 Intermediate calculations Standard Error of the Mean 3 Z Test Statistic 1.5 Upper-Tail Test Upper Critical Value 1 6449 p-Value 0.0568 Do not reject the null hypothesisCOMPUTE_ALL Z Test for the Mean Data Null Hypothesis Level of Significance population Standard Deviation 15 Sample Size 25 Sample Mean 372 5 Intermediate calculations Standard Error of the Mean Z Test Statistic 1.5 Two-Tail Test Lower Critical Value -1.9500 Upper Critical Value 1.9500 p-Value 0.1536 Do not reject the null hypothesis Lower-Tail Test Lower Critical Value -1.6449 p-Value 0.9332 Do not reject the null hypothesis Upper-Tail Test Upper Critical Value 1 8449 p-Value 0.0864 Do not reject the null hypothesisCOMPUTE AL Z Test for the Mean Data Null Hypothesis 980 Level of significance Population Standard Deviation 15 Sample Size 25 Sample Mean 372.5 Intermediate calculations Standard Error of the Mean Z Test Statistic 1.5 Two-Tail Test Lower Critical Value -1 9600 Upper Critical Value 1 9600 p-Value 0.1336 Do not reject the null hypothesis Lower-Tail Test Lower Critical Value -1 6449 p-Value 0.9332 Do not reject the null hypothesis Upper-Tail Test Upper Critical Value 1.84 49 p-Value 0.0860 Do not reject the null hypothesis