. A large university system states that the mean expenses for books and supplies

Question

. A large university system states that the mean expenses for books and supplies are $1200.00 on average for its students. In view of the rising text book costs, a student advocacy agency suspects that it may be higher. They are going to take a simple random sample of 40 students and conduct a test at a 5% level of significance for 1200 1200 : $ : $ A O H H Given that the population standard deviation is $100 Find the probability of committing a type II error if in fact a) $1225 b) $1250

Please show all work.

Explanation / Answer

std error =std deviation/(n)1/2 =100/(40)1/2 =15.81

here for one tailed test; and 0.05 level; critical value of z =1.645

therefore corresponding critical value =mean +z*std deviation =1200+1.645*15.61=1226.01

therefore probability of committing a type II error =P(X<1226.01)=P(Z<(1226.01-1250)/15.81)

=P(Z<-1.5174)=0.0646

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