Question

12. What is the lifespan of light bulbs? Test the claim that the mean is less than 230 hours using a 0.05 significance level. A random sample of 34 has a mean of 226.4 hours and a standard deviation of 19.8 hours.

a. Give the critical region and the value of the test statistic.

b. Give the decision and conclusion.

Answer 1

Solution :

Given that:

= 226.4 hours

s = 19.8 hours

n = 34

a.) Hypothesis:

H0 : 230 hours

Ha :   230 hours

Test Statistic:

t = ( - ) / (s /n)

t = (226.4 - 230) / ( 19.8 / 34)

t = -1.060

crtical value:

degrees of freedom = d.f= n-1 = 34 - 1= 33

level of significance

= 0.05

tc = -1.692

P - value = 0.1484

b.) if P- value < 0.05 then reject H0.

P-value > 0.05, we Fail to reject H0.

There is not sufficient evidence to support to claim.