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 with mu = 100 min and sigma = 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: mu = 100 Ha: mu > 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 above scenario. What is your decision for the above hypothesis test if alpha error is maintained at 0.05? upper tail test Reject the null hypothesis if x-bar>= 102.05 type I error 0.154184 What is the P-value for the test in part (a) What is the alpha error for the test procedure that "rejects H0 if the test statistic (Z0) is greaterthanorequalto 1.35" 0.911492009 Will the decision for the hypothesis in part (a) change if the sample size n = 60 (assume no other changes in the data) Show your work for your answer 0.0388357715

Explanation / Answer

This is upper tail test
For rejection region in the form of drying time
xbar = mean + z*sigma/(sqrt(n))
Here mean = 100, z (for 95%) = 1.64 , sigma = 9 and n = 20

xbar = 100 + 1.64*9/sqrt(20) = 103.3

Reject null hypothesis if xbar >= 103.3
Type I error = 0.05

Test statistics, z = (102.05-100)/(9/sqrt(20)) = 1.01865

p-value = 0.154184

For z=1.35, find probability
P(z<1.35) = 0.91149

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