The Professor's Response
Hi professor, I am also stuck in 46 in section 8.6.
when i am finding p̂, i do not know if i do 15/100 or if its just 15.
If i use 15/100 in the formula to calculate the test statistic i get -1.40 and that is not correct? would you not do that for this problem?
thank you
See the professor's answer below.
A professor claims that at most 10% of the class gets A’s each semester in his course. A random sample of 100 students from previous terms show that he gave out 15 A’s. Using a 5% significance level, test the professor’s claim.
Claim: p ≤ 0.10
Ho: p ≤ 0.10
Ha: p > 0.10
n = 100
x = 15
p-hat = x/n = 15/100 = 0.15
alpha = 5%
Test stat: (0.15 - 0.10) / Root(0.10 * 0.90 / 100) = 1.66666667 = 1.67
Critical value: 1.645
Reject H0, support Ha
We reject the claim since it is the same as H0 and we are rejecting H0.
Hope that helps,
Professor McGuckian
I think you are asking about the critical value because you cannot use the t-table to find a p-value (not an exact one anyway).
Remember that the t-table has z-values in the last row, so we almost always use the t-table to find critical z-values. If the sample size is large, we go to the last row of the table. If the sample size is small, we only go down to the appropriate degrees of freedom.
Of course, it is possible that your alpha value will not be on the t-table if your sample size is large because only 5 alpha values can be found on the t-table. If that happens, you will use the z table. Section 8.2 covers this with several examples.