37. A study was instituted to learn how the diets of women changed during the winter and the summer. A random group of 12 women were observed during the month of July and the percentage of each woman’s calories that came from fat was determined.

Similar observations were made on a different randomly selected group of size 12 during the month of January. The results were as follows

Test the hypothesis that the mean fat percentage intake is the same for both months.
Use the

(a) 5 percent level of significance and

(b) 1 percent level of significance.

July January 30.5, 28.4, 40.2, 37.6, 36.5, 38.8, 34.7, 29.5, 29.7, 37.2, 41.5, 37.0 32.2, 27.4, 28.6, 32.4, 40.5, 26.2, 29.4, 25.8, 36.6, 30.3, 28.5, 32.0