The drying time of a certain type of paint under specified test conditions is co

Question

The drying time of a certain type of paint under specified test conditions is considered to be normally distributed witn =100 min and =9 min.
It is suspected that the actual drying time is perhaps higher than 100 min. and hence a hypothesis test is being arranged as
H0: µ = 100
Ha: µ >100
n=20 random samples have been collected and drying time measured for each.
Average drying time calculated from the samples is X-bar= 102.05 min
Answer the following questions for the aboove scenario.
a)What is your decision for the above hypothesis test if error is maintained at 0.05?
b)What is the P-value for the test in part (a)
c)What is the error for the test procedure that "rejects H0 if the test statistic (Z0) is 1.35"
d)Will the decision for the hypothesis in part (a) change if the sample size n= 60 (assume no other changes in the data)

I need i know what equations I need to use for each part, it would be perfect if I get the answers in excel format.

Explanation / Answer

Using Minitab:

One-Sample Z

Test of = 100 vs > 100
The assumed standard deviation = 9

N Mean SE Mean 95% Lower Bound Z P
20 102.05 2.01 98.74 1.02 0.154

a. P-value =0.154 >0.05 so we do not reject the null hypothesis.

b.0.154

d.

One-Sample Z

Test of = 100 vs > 100
The assumed standard deviation = 9

N Mean SE Mean 95% Lower Bound Z P
60 102.05 1.16 100.14 1.76 0.039

Yes.The decision for the hypothesis in part (a) change if the sample size n= 60 .

P-va;ue < 0.05 we reject null hypothesis.

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