Question

Average life of light bulbs produced by SABA Electric Co. is believed to be normally distributed with the mean service life of 1200 hours and a standard deviation of 78 hours. A random sample of 169 bulbs is tested and it has a mean life of 1100 hours. Can we conclude that the mean service life of the bulbs is less than the expectation at 98% level of confidence?

a. Yes. The mean service life of the bulbs is less than the expectation.

b. No. The mean service life of the bulbs is not less than the expectation.

c. Both a and b are correct.

d. None of the above.

Answer 1

H0: = 1200

Ha: < 1200  

Test statistics

z = - / ( / sqrt(n) )

= 1100 - 1200 / (78 / sqrt(169) )

= -16.67

This is test statistics value.

p-value = P( Z < z)

= P (Z < -16.67)

= 0

At 0.02 significance level, since p-value is less than 0.02 level, we have sufficient evidence to reject H0.

We conclude at 0.02 level that we have enough evidence to support the claim.

Yes. The mean service life of the bulbs is less than the expectation.

[ Confidence interval method.

CI = t * S / sqrt(n)

That is

- t * S / sqrt(n) < < + t * S / sqrt(n)

1100 - 2.326 * 78 / sqrt(169) < < 1100 + 2.326 * 78 / sqrt(169)

1086.044 < < 1113.956

CI = (1086.044 , 1113.956)

Since claimed mean 1200 is not contained in confidence interval, we conclude that mean is less than expectation.]