Question

The quality control division of a factory that manufactures batteries suspects defects in the
production of a model of mobile phone battery which results in a lower life for the product.
Until now, the time duration in phone conversation for the battery followed a normal
distribution with a mean of 300 minutes. However, in an inspection of the last batch produced
before sending it to market, it was found that the average time spent in conversation was 290
minutes in a sample of 20 batteries with a standard deviation of 30 minutes. Assuming that the
time is normally distributed, can it be concluded that the quality control suspicions are true at a
significance level of 1%? Construct the 99% confidence bound for the average life of electric
lamps and relate it to the result of the hypothesis test

Answer 1

(a)

H0: Null Hypothesis: 300 ( the average time spent in conversation was not less thsn 300 minutes )

HA:Alternative Hypothesis: 300 ( the average time spent in conversation was less thsn 300 minutes) (Claim)

n -=20

So,

df = 20 - 1 = 19

=0.01

From Table, critical value of t = - 2.539

Test Statistic is given by:

Since calculated value oft = - 1.491 is greater than critical value of t = - 2.539, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support theclaim that the average time spent in conversation was less thsn 300 minutes.