Question

Please answer this. Thank you

1. A company manufactures gas bottles for industrial use and claims that the average hours of use is 500 hours. A purchaser of these bottles doubts the claims and believes the use time is less than 500 hours. To test the manufacturers, claim the purchasing agent randomly selects six of these gas bottles from the manufacturer and finds that the sample average is 493 hours with a sample standard deviation of4 hours Assuming that the population is normally distributed, test if the manufacturers claim is justified at the 0.05 level of significance? (30)

Answer 1

H0: Null Hypothesis: $\mu \geq$ 500

HA: Alternative Hypothesis: $\mu <$ 500

SE = s/ $\sqrt{n}$

= 4/ $\sqrt{6}$ = 1.6330

Test statistic is:

t = (493 - 500)/1.6330 = - 4.2866

$\alpha$ = 0.05

ndf = 6 - 1 = 5

One Tail - Left Side Test

From Table, critical value of t = - 2.0150

Since the calculated value of t = - 4.2866 is less than critical value of t = - 2.0150, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the use time is less than 500 hours.