Step 1:
Ho. P<=20%, H1. P>20%
Step 2:
Type I error occurs when a true H0 is rejected which means that the people who remember the ad are
>20% and Type II error occurs when a false H0 is not rejected which means P<=20% and H0 is rejected
when P-value < Alpha.
The local radio station plans to conduct this test using a 10% level of significance, but the company wants
the significance level lowered to 5% because if you reduce the significance level (from 0.1 to 0.05), the
region of acceptance gets bigger. As a result, you are less likely to reject the null hypothesis. This means
you are less likely to reject the null hypothesis when it is false, so you are more likely to make a Type II
error.
Step 3:
p = no. of people who remember the ad = 113,
q = no. of people who don't remember the ad = 487,
n = 600 and alpha = 5%
Now, p hat = 113/600 = 18.83 %
In JMP per the snip below, we have arrived at the P-value of 0.7625 and when compared to Alpha, it is
greater than it which means a false H0 is not rejected which is a Type II error.
Thus, the company will not renew the contract.
