Question

Light bulbs of a certain type are advertised as having an averagelifetime of 750 hours. The price of these bulbs is very favorable,so a potential customer has decided to go ahead with a purchasearrangement unless it can be conclusively demonstrated thatthe true average lifetime is smaller than what is advertised. Arandom sample of 50 bulbs was selected, the lifetime of each bulbdetermined, and the appropriate hypothesis were tested usingMINITAB, resulting in the accompanying output.

Variable N Mean St Dev SEMean ZP -Value
lifetime 50 738.44 38.20 5.40-2.14 0.016

What conclusion would be appropriate for a significance level of.05 ? .A significance level of .01 ?. What significance level wouldyou recommend ?

Answer 1

Customer will not purchase the light bulbs at significance level of 0.05

Customer will purchase the light bulbs at significance level of 0.01 .

Explanation:

We are given that Light bulbs of a certain type are advertised as having an average lifetime of 750 hours. A random sample of 50 bulbs was selected, and the following information obtained:

Variable N Mean S.D. SE of Mean Z P -Value

lifetime 50 738.44 38.20 5.40 -2.14 0.016

Let Null hypothesis,
`H_0` :
`\mu` = 750 {means that the true average lifetime is same as what is advertised}

Alternate Hypothesis,
`H_1` :
`\mu` < 750 {means that the true average lifetime is smaller than what is advertised}

Since we are given that P-value is 0.016.

The Decision rule states that ;

If P-value is less than the significance level ⇒ Reject null hypothesis

If P-value is more than the significance level ⇒ Accept null hypothesis

(a) Now, at 5% significance level, we know that the p-value is less than the significance level as 0.016 < 0.05 so we have sufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is smaller than what is advertised and so consumer will not purchase the light bulbs.

(b) Now, at 1% significance level, we know that the p-value is more than the significance level as 0.016 > 0.01 so we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is same as what it has been advertised and so consumer will purchase the light bulbs.

So, we will recommend a significance level of 0.01 as only then customer will purchase the light bulbs.