As one of their selling points, an Illinois state university claims their averag

Question

As one of their selling points, an Illinois state university claims their average class size is 24 students or fewer. A bureaucrat in the Illinois Department of Education believes the university may be overselling this and that the average class size is actually more than 24 students. To test her belief, she randomly samples 45 class rosters from the school's registrar's office. This results in a sample mean classroom size of 24.9 students with a sample standard deviation of 3.3 students. At the 01 level of significance, is there enough statistical evidence to support her belief that the schools average class size exceeds 24 students? Class size is assumed to be normally distributed. List and clearly label all eight steps. Round to 4 decimal places.

Explanation / Answer

CLAIM:

MEAN>24

step1:

state null and alternative hypothesis

Ho: mean=24

H1: mean>24

step2:state level of significance

alpha=0.01

step3:

calculation of test statistic:

z=sample mean-pop mean/samplesd/sqrt(samplesize)

=24.9-24/3.3/sqrt(45)

z cal =1.8295

step4:

Decsion rule:

if z cal>z crit at 5% level of significance reject null hypothesis

if   z cal<z crit at 5% level of significance fail to reject null hypothesis

step5:

calculation of z critical

z crit for 95%=1.96

step6:

statistical decsion:

since zcal < zcrit

fail to reject null hypothesis

Step7:

conclusion:

There is no sufficient statistical evidence at 5% level of signiifcance to support the claim thta t the schools average class size exceeds 24 students.

  

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