Question

# A manufacturer claims that the mean lifetime, u, of its light bulbs is 53 months. The...

A manufacturer claims that the mean lifetime, u, of its light bulbs is 53 months. The standard deviation of these lifetimes is 6 months. Ninety bulbs are selected at random, and their mean lifetime is found to be 52 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 53 months?

Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table.

The null hypothesis:

The alternative hypothesis:

The type of test statistic: (choose one, z,t,chi square,f)

The value of the test statistic:
(Round to at least three decimal places.)

The two critical values at the 0.05 level of significance:
(Round to at least three decimal places.)   ______ and _______

Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 53 months? Yes or No

given data are:-

sample mean () = 52

sample size (n) = 90

population sd () = 6

a).The null hypothesis:-

b).The alternative hypothesis:-

c).The type of test statistic: z

[ as here, the population sd is known ]

d).The value of the test statistic:-

e).The two critical values at the 0.05 level of significance: -1.960 and 1.960

f).NO, we can not conclude that the mean lifetime of light bulbs made by this manufacturer differs from 53 months.

[ ....so, we fail to reject the null hypothesis.]

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