Question

A company manufacturing light bulbs is testing a new model. The company claims that the mean life time is less than 1000 hours.

A sample of 16 light bulbs are found to have sample mean of 987.5 hours and a sample variance of 400.

(a) Test this claim at the significance level α = 0.02.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

(b) Is there any assumption needed to solve this question? if yes please state the assumption

Answer 1

Step 1:

Ho: ≥ 1000  

Ha: < 1000 (Claim)

Step 2: Test statistics

n = 16

sample mean = 987.5

sample varaince = 400

sample sd = 20

Assuming that the data is normally distribited, also as the population sd is not given, we will use t stat

p value = 0.0123

Step 3: Rejection region

= 0.02

t critical for left tailed test = - 2.24854029

If t stat is less than -2.249, the null hypothesis is rejected.

Step 4: Decision :

As the t stat ( -2.50) is less than t critical (-2.249), the Null hypothesis is rejected.

Also as the p value (0.0123) is less than ( 0.02), the Null hypothesis is rejected.

Step 5: Conclusion:  

Hence there is sufficient evidence to believe that the mean life time is less than 1000 hours at significance level = 0.02

(b) Is there any assumption needed to solve this question? if yes please state the assumption

Assuming that the data is normally distributed.