Question

Suppose that you have to decide if the mean of the light bulbs last longer than 150 hours. You choose a random sample of 10 bulbs of each brand. What decision should you make at the 5% significance level (alpha = 0.05)?

       128     189     139     148     186     141     163     101     195     142  

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

Null hypothesis: H₀: The mean of the light bulbs last is 150 hours.

Alternative hypothesis: H_a: The mean of the light bulbs last longer than 150 hours.

H₀: µ = 150 versus H_a: µ > 150

This is an upper tailed or right tailed (one tailed) test.

We are given level of significance = α = 0.05

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

Sample mean = Xbar = 153.2

Sample standard deviation = S = 29.93251669

Sample size = n = 10

df = n – 1 = 10 – 1 = 9

Critical value = 1.8331

(by using t-table)

t = (153.2 - 150)/[ 29.93251669/sqrt(10)]

t = 3.2/9.4655

t = 0.3381

P-value = 0.3715

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that the mean of the light bulbs last longer than 150 hours.