Question

The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,520 hours. The population standard deviation is 840 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,340 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,520 hours? b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach? a. Let y be the population mean. Determine the null hypothesis, Ho, and the alternative hypothesis, H Ho: μ: 7520 H: H 7520 What is the test statistic? Test Statisitc1.5 Round to two decimal places as needed.) What is/are the critical value(s)? Round to two decimal places as needed. Use a comma to separate answers as needed.) What is the final conclusion? A. Fail to reject Hn. There is not sufficient evidence to prove that the mean life is different from 7,520 hours.

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test: H : Mean of population Ho : μ 7520 Ha : μ # 7520 Standard deviation 840 Hypothesis test results: Mean n Sample Mean Std. Err. Z-Stat P-value H 49 7340 120 1.5 0.1336

95% confidence interval results: Mean n Sample Mean Std. Err. L. LimitU. Limit 49 7340 120 7104,8043 7575.1957

Hence,

a) Hypotheses:

H₀ : μ = 7520
H_A : μ ≠ 7520

Test statistic = -1.50

Critical values = -1.96, 1.96

Conclusion: Option A is correct.

b) p - Value = 0.134

Meaning of p - value: Option D is correct.

c) 95% confidence interval:

7104.8 $\leq \mu \leq$ 7575.2

d) Option D is correct.