Question

5. Suppose that you want to decide which of two equally-priced brands of light bulbs lasts longer. You choose a random sample of 100 bulbs of each brand and find that brand Δ has a sample mean 150 hours and a sample standard deviation of 70 hours, and that brand B has sample mean of 1170 hours and sample standard deviation of 80 hours. What decision should you make at 2% significance level?

Answer 1

Ans:

$H_0:\mu _1\geq \mu _2$

$H_a:\mu _1< \mu _2$

Assumption:Unequal population variances.

Test statistic:

t=(1150-1170)/sqrt((70^2/100)+(80^2/100))

t=-1.881

df=100-1=99

p-value=tdist(1.881,99,1)=0.0315

As,p-value>0.02,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that second brand lasts longer.