An electrical firm manufactures light bulbs that have a lifetime that is approximately normally distributed with a mean of 800 hours and a s

Question

An electrical firm manufactures light bulbs that have a lifetime that is approximately normally distributed with a mean of 800 hours and a standard deviation of 40 hours. Test the hypothesis that μ = 800 hours against the alternative, μ = 800 hours, if a random sample of 30 bulbs has an average life of 788 hours. Use a P-value in your answer.

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1 week 2021-09-15T04:38:41+00:00 1 Answer 0

If we compare the p value and a significance level for example we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the lifetime is not signficantly different from 800 hours.

Step-by-step explanation:

Data given and notation

represent the average life for the sample

represent the population standard deviation

sample size

represent the value that we want to test

represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to apply a two tailed  test.

What are H0 and Ha for this study?

Null hypothesis:

Alternative hypothesis :

Compute the test statistic

The statistic for this case is given by:

(1)

z-test: “Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value”.

Calculate the statistic

We can replace in formula (1) the info given like this:

Give the appropriate conclusion for the test

Since is a one side left tailed test the p value would be:

Conclusion

If we compare the p value and a significance level for example we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the lifetime is not signficantly different from 800 hours.