Answer to Question #307940 in Statistics and Probability for Ida

Question

Two years ago, 75% of a financial bank’s customers were satisfied with the service provided by the bank. The bank manager would like to test if the percentage has changed over the time.

a) What hypothesis should be tested?

b) From a survey on 20 random samples, 13 customers are satisfied. Determine the rejection region at .

c) Calculate p-value.

d) If the probability of incorrectly rejecting a true H0 is 0.01, what decision shall you obtain?

A type of treatment has been identified to produce cement compression strength of 5000 kg/cm² with a standard deviation of 120. To test the null hypothesis that  = 5000 against the alternative hypothesis that  < 5000, a random sample of 50 pieces of cement was tested. The rejection region is defined as x < 4970.

a) Define Type I and Type II Error for the testing.

b) Calculate the probability of Type II Error if  = 4960.

c) What is the power of the test?