# Mean Lifetime of Light Bulbs

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A manufacturer claims that the mean lifetime of its light bulbs is 51 months. The standard deviation of these lifetimes is 5 months. Fifty bulbs are selected at random, and their mean lifetime is found to be 50 months. Can we conclude....(see attached)

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##### Solution Summary

A manufacturer claims that the mean lifetime, , of its light bulbs is months. The standard deviation of these lifetimes is months. Fifty bulbs are selected at random, and their mean lifetime is found to be months. Can we conclude, at the level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 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: H : ____

0

The alternative hypothesis: H : _____

1

The type of statistic: a. Z

b. t

c. Chi square

d. F

The value of the test statistic: ______

(Round your answer to at least

three decimal places.)

The two critical values at the 0.1 level of significance: _____

(Round your answer to at least

three decimal places.)

Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 51 months? Yes or No?

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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