Question

Suppose the manufacturer claims that the mean lifetime of a light bulb is more than 10,000 hours. In a sample of 30 light bulbs, it was found that they only last 9,900 hours on average. Assume the population standard deviation is 120 hours. At 0.05 significance level, can we reject the claim by the manufacturer?

Select one: a. We reject the claim b. We accept the claim

Answer 1

According to the question,

Mean life time of a light bulb($\mu$₀)>10,000 is assumed by the manufacturer.

sample mean($\bar{x}$) of the light bulb=9900

population standard deviation($\sigma$)=120 hours

sample number of light bulbs=30

Now, carry out the test,

H₀: $\mu$ =$\mu$₀

H₁:$\mu$>$\mu$₀

We will reject null hypothesis and accept that the average life time of the bulb is more than 10000 is calculated
7
₀>0.05(tabulated
7
)

Here, we have to carry out test.

7

7
₀=$\frac{\sqrt{n}(\bar{x}-\mu )}{\sigma }$

=$\frac{\sqrt{30}(9900-10000)}{120}$

=-4.56

Hence, we find that, calculated
7
₀<tabulated
7
i.e, -4.56<0.05, So , we will accept H₀ and reject the claim that average life time of the bulbs is more than 10000.

Therefore, We will reject the claim.