Question

A consumer claims that the mean lifetime of a brand of fluorescent bulbs is less than1500 hours. She selects 25 bulbs and finds the mean lifetime to be 1480 hours with the standard deviation of 80 hours. If you were to test the​ consumer's claimat the 0.05 significance​ level, what would you​ conclude?

Answer 1

We conclude that the mean lifetime of a brand of fluorescent bulbs is equal to 1500 hours.

Explanation:

We are given the following in the question:

Population mean, μ = 1500 hours

Sample mean,
`\bar{x}` = 1480 hours

Sample size, n = 25

Alpha, α = 0.05

Sample standard deviation, s = 80 hours

First, we design the null and the alternate hypothesis

`H_(0): \mu = 1500\text{ hours}\\H_A: \mu < 1500\text{ hours}`

We use one-tailed(left) t test to perform this hypothesis.

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }`

Putting all the values, we have

`t_(stat) = \displaystyle(1480-1500)/((80)/(√(25)))= -1.25`

Now,

`t_(critical) \text{ at 0.05 level of significance, 24 degree of freedom } = -1.71`

Since,

`t_(stat) > t_(critical)`

We fail to reject the null hypothesis and accept the null hypothesis.

We conclude that the mean lifetime of a brand of fluorescent bulbs is equal to 1500 hours.