Question

A random sample of 50 Business school applicants in a university records a mean of 31 points on the multiple-choice university admissions test. A student says that the mean is actually more than 30 points. Assume the population standard deviation is given as 2.5 points

The appropriate hypothesis statements and claim is … ..............Answer 1 Choose...

The appropriate Z-score is calculated to be…............................... Answer 2 Choose...

If we say alpha is 0.05, it then means that …. .....................................Answer 3 Choose...

Using alpha=0.05, the appropriate P-values for this test is....................Answer 4 choose

4 Choose... From results obtained so far, it is valid to …........................answer 5

Answer 1

sample size = n = 50

mean = 31 points

population standard deviation = 2.5 points

Here hypothesis is

H0 : = 30

Ha :   30

standard error = 2.5/sqrt(50) = 0.3536

Z = (31 - 30)/0.3536 = 2.8284

If alpha mean 0.05 that means that we will reject the null hypothesis at for maximum probability 0.05, when null hypothesis is correct.

P value = P(z > 2.8284) = 1 - 0.9977 = 0.0023

Here null hypothesis is rejected and can be said that mean is greater than 30.