I need B and C please The shelf life of a photographic film

I need B and C please

The shelf life of a photographic film is of interest of the manufacturer. The manufacturer observes the following shelf life for eight units chosen at random from the current production. Assume that the shelf life is normally distributed. a. Is there evidence at a $% level of significance that the mean shelf life is greater than or equal to 125 days? b. If the true shelf life is 132 and we wish to have a power of 0.8, what sample size should we use? c. If the sample size calculated in part b) is used, what is the power of the test if we want to detect a shift on the mean by one standard deviation?

Solution

Given that X = shell life is normal

Sample size = 8

As population std deviation is not known we use t test to test the mean.

The sample mean = 129.5

Std dev = 12.242

Std error = 4.627

a) H0: mu = 125

Ha: Mu >125

(Right tailed test at 5% level)

Mean diff = 129.5-125=4.5

t statistic = 4.5/std error =0.9725

df = 7

p value =0.3632

As p>alpha, accept null hypothesis.

There is no evidence to prove the mean >=125 days

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When sample average = 132, power = 0.8

sample size should be 21 or 22

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Margin of error = 1 std deviation

= 4.627

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Sample size 12 should be used .