Bookstores like education, because national data show that 71% of college graduates have read a book in the past year, compared to 54% of the general population age 18 and over.
The data also show the nationwide average educational level to be 13 years of schooling completed, with a SD of about 3 years, for persons age 18 and over. A bookstore is doing a market survey in a certain county and takes a simple random sample of 1,000 people age 18 and over. They find the average educational level to be 14 years, and the SD is 5 years.
a) What is the null hypothesis? (A) The average educational level of the sample is the same as the average education level in the nation. (B) The average educational level of the sample is different from the average education level in the nation.
I think is A, but I am not sure.
b) Can the difference in average educational level between the sample and the nation be explained by chance variation? (A) Yes (B) No
My calculations: The SE for the average is √1000×51000≈0.16. The z-statistic is z=14-130.16≈6,the P-value is 0%. The average educational level in the county is higher than 13 years. So, is it (A) Yes?