For the following question : State the null and alternative hypothesis. Select t

Question

For the following question :

State the null and alternative hypothesis.
  Select the distribution to use.
Write the decision rule. (Define the rejection region.)
Calculate the test statistic.
Calculate the p-value.
Make a decision. (Additional step for this worksheet) State the type I and II error in context of the problem.

It has been reported that the average credit card debt for college seniors at the college
book store for a specific college is $3262. The student senate at a large university
feels that their seniors have a debt much less than this, so it conducts a study of 50
randomly selected seniors and finds that the average debt is $2995 with a standard
deviation is $1100. With an = 0.01, is the student senate correct?

Explanation / Answer

H0: mu=3262

H1:mu<3262

since sample size is large, we use normal distirbution.

the critical value is -2.3263. The region beyond this is the rejection region.

z=xbar-mu/sd/sqrt(n)=-1.72

p=0.0430

since p >0.01, we reject the null hypothesis.

if the null hypothesis is true and we reject it, then it is type 1 error.

if the null hypothesis is false and we accept it, then it is type 2 error.

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