Question

Please solve using minitab and explain steps. Please show all work

9.14 The quality-control manager at a light emitting diode (LED) factory needs to determine whether the mean life of a large shipment of LEDs is equal to 50,000 hours. SELF TEST

Answer 1

Claim: Mean life of shipment of LED's is 50000 hours that is

μ = 50000

Step 1: To write the null and alternative hypothesis

Step 2: Test statistics

Here the population standard deviation is known so the z test is applicable.

The formula of test statistics is

Where

Step 3: Critical value

Here the alternative hypothesis contains not equal to sign so the test is two tailed test.

There are 2 critical values both are same just opposite in sign.

Here alpha (level of significance) = 0.05

Alpha/2 = 0.05/2 = 0.025

Search 0.025 in the middle body of table and then take the corresponding z score. The corresponding z score is -1.96

So the Critical values are -1.96 and 1.96

Step 4: Decision rule

If test statistics falls between both the critical values then we fail to reject the null hypothesis otherwise we reject the null hypothesis.

Here test statistics -0.67 falls between -1.96 and 1.96, so we fail to reject the null hypothesis.

Step 5: Conclusion

Fail to reject the null hypothesis, that is there is no sufficient evidence that the mean life is different from 50000 hours.