Question

1. A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1500 hours. A homeowner selects 40 bulbs and finds the mean lifetime to be 1480 hours with a population standard deviation of 80 hours. Test the manufacturer's claim. Use alpha equal to 0.05. State the sample mean and the population standard deviation.
2. Using problem in number 1. Choose the correct hypotheses.
3. Using the problem in number 1. State the critical value(s).
4. Using the problem in number 1. State the Test Statistics.

A.) -1.96
B.) -2.00
C.) 1.58
D.) -1.58

5. Using the problem in number 1. State the decision.

A.) fail to reject Ha
B.) Reject H0
C.) Reject Ha
D.) fail to reject H0

6. Using the problem in number 1. State the conclusion.

A.) There is not enough evidence to support the claim that the mean lifetime of its fluorescent bulbs is 1500 hours.
B.) There is enough evidence to support the claim that the mean lifetime of its fluorescent bulbs is 1500 hours.
C.) There is not enough evidence to reject the claim that the mean lifetime of its fluorescent bulbs is 1500 hours.
D.) There is enough evidence to reject the claim that the mean lifetime of its fluorescent bulbs is 1500 hours.

Answer 1

Answer:

(1) Sample mean is 1480 hours and population standard deviation is 80 hours

(2) Null hypothesis: The mean lifetime of its fluorescent bulbs is 1500 hours

Alternate hypothesis: The mean lifetime of its fluorescent bulbs is less than 1500 hours

(3) 1.645

(4) D

(5) B

(6) A

Step-by-step explanation:

(1) From the population parameter, the sample mean is 1480 hours and population standard deviation is 80 hours

(2) The null hypothesis is statement deduced from the population parameter which is tested to be true or false

The alternate hypothesis is also a statement from the population parameter that negates the null hypothesis

(3) Using the standard normal distribution table, the critical value of one tailed test with significance level of 0.05 is 1.645

(4) Z = (sample mean - population mean)/(sd/√n)

sample mean = 1480, population mean = 1500, sd = 80, n = 40

Z = (1480 - 1500)/(80/√40) = -20/12.65 = -1.58

(5) The null hypothesis is rejected because the test statistic -1.58 is less than the critical value 1.645

(6) There is not enough evidence to support the claim that the mean lifetime of its fluorescent bulbs is 1500 hours because the null hypothesis is rejected