Question

2. (a) From a store containing 50 masonry drill bits 25 were used without replacement and found to have a mean life of 15 hours with a standard deviation of 2.5 hours. Does the data suggest that the mean life of the bits is greater than 14 hours? Use level of significance (a =0.05). (5 marks)

Answer 1

Answer:

n=25 , $\bar x$ = 15, s = 2.5, $\mu$ =14,  $\alpha$=0.05

Null and Alternative hypothesis is

Ho: $\mu$ $\leq$ 14

H1: $\mu$ > 14

calculate test statistics

- s/n

15 – 14 2.5/725

t = 2

test statistics = 2

now calculate P-Value we get

P-Value = 0.0285

calculate t critical value for right tailed test with df = n-1 =25-1 =24

using t table we get t critical value as

t critical value = 1.711

since , (test statistics = 2 ) > ( t critical value = 1.711 )

the null hypothesis is rejected.

Conclusion:

Therefore,  there is enough evidence to claim that the mean life of bits is greater than 14.