The quality-control manager at a compact fluorescent light bulb (CFL) factory ne

Question

The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean ife of a large shpment of CFLsal to 7 869 hours The popuilation standand deviation is 900 hours A random sample of 81 light bulbs indicates a sample mean life of 7 219 hours a. At the 0 05 level of signišicance, is there evidence that the mean lide is different from 7,.469 hours b. Compute the p-value and interpret its meaning e. Construct a 95% confidence iterval estimate of the population mean lfe of the Ight bubs d. Compare the results of (a) and (c) What conclusions do you reach? a. Let be the population mean Determine the rul hypothesis Ho and the alernative hypothesis H, H, m, , What is the test statistic? ZgTAT (Round to two decimal places as needed ) What is/are the critical vaks)? Click to select your answers

Explanation / Answer

The provided sample mean is X¯=7219 and the known population standard deviation is =900, and the sample size is n=81.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: =7469

Ha: 7469

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is =0.05, and the critical value for a two-tailed test is zc=1.96.

The rejection region for this two-tailed test is R={z:|z|>1.96}

(3) Test Statistics

The z-statistic is computed as follows:

z=x-mu/(s/sqrt(n)) = 2.5

(4) Decision about the null hypothesis

Since it is observed that |z|=2.5>zc=1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0124, and since p=0.0124<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean is different than 7469, at the 0.05 significance level.

Confidence Interval

The 95% confidence interval is 7023.004<<7414.996.

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