Part II The significance level for hypothesis testing is 0.05, unless otherwise specified.(50%)

1. (10%) 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. Suppose the results were as follows:

July: mean =30.83, standard deviation=4.30

January: mean =35.13, standard deviation=4.51

If we assume the population standard deviations for all months are equal, conduct a test for testing the hypothesis if the mean fat intake is the same for both months.