Question

I need the answer to the following, but not using the P value.

4. A librarian claims that the mean number of books read per year by community college students is more than 2.5 books. A random sample of 33 community college students had read a mean of 3.2 books with a standard deviation of 1.9 books. Test the librarian's claim at the 0.01 level of significance.

5. A reading group claims that Americans read more as they grow older. A random sample of 45 Americans age 60 or older read for a mean length of 62.8 minutes per day, with a population standard deviation of 18.3 minutes per day. A random sample of 88 Americans between the ages of 50 and 59 read for a mean length of 57.2 minutes per day, with a population standard deviation of 23.1 minutes per day. At the 0.05 level of significance, test the claim that the mean time spent reading per day by Americans age 60 and older is longer than the mean time spent reading per day by Americans between the ages of 50 and 59.

6. A car manufacturer advertises that a certain model has a variance in miles per gallon equal to 12.25. A car magazine wanted to check the advertisement and collected a random sample of 15 cars to test and found the variance in miles per gallon equal to 17.64. At the 0.05 level of significance, test the magazine's claim that the variance is different from 3.5 miles.

Answer 1

4. Here claim is that the mean number of books read per year by community college students is more than 2.5 books.

So hypothesis is vs

As population standard deviation is not known, we will use t distribution to find test statistics

The t-critical value for a right-tailed test, for a significance level of α=0.01 is

tc​=2.449

Graphically

As t statistics is not in the rejection region, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that the mean number of books read per year by community college students is more than 2.5 books.