Fowle Marketing Research, Inc., bases charges to a client on the assumption that

Question

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed within 15 minutes. If more time is required, a premium rate is charged. With a sample of 35 surveys, a population mean is 17 minutes and standard deviation of 4 minutes, and a level of significant of.01, the sample mean will be used to test the null hypothesis Ho: mu = 15 1) Formulate null and alternative hypotheses to test the Fowle Marketing Research's claim. 2) Conduct your hypothesis test using alpha = 0.01 as the level of significance. What is your conclusion? 3) What is your interpretation of the Type I error and Type II error for this problem? 4) How do you control Type I error and Type II error?

Explanation / Answer

here null hypothesis: mean =15

alternate hypothesis: mean >15

2) here std error =(std deviaition/(n)1/2 =0.676

hence test stat z=(X-mean)/std error =(17-15)/0.676=2.958

for above p value =0.0015

as p value is less then 0.01 level, we reject that mean is 15, and hence marketing research claim needs to be rejected,

3)type I error is rejecting marketing claim when true

type II error: accepting claim when it is false

4) it can be controlled by increasing sample size.

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