1.(10 points) If we increase our food intake, we generally gain weight. Nutrition scientists can calculate the amount of weight gain that would be associated with a given increase in calories. In one study, 16 nonobese adults, aged 25 to 36 years, were fed 1000 calories per day in excess the calories needed to maintain a stable body weight. The subjects maintained this diet for 8 weeks, so they consumed a total of 56,000 extra calories. According to theory, 7700 extra calories will translate into a weight gain of 1 kilogram. Therefore, we expect each of these subjects to gain 56000/7700=7.3 kilograms. The weights in kilograms before and after the 8-week period are shown below:

ID:1234567 8910111213141516

Before:55.754.959.662.374.275.670.753.373.363.468.173.791.755.961.757.8

After:61.758.866.066.279.082.474.359.379.166.073.476.993.163.068.360.3

(1)For each subject, manually calculate the weight gain subtracting the weight before from the weight after.

(2)Manually find the mean and the standard deviation for the weight gain in your output and report/paste it here

(3)Calculate the standard error and the margin of error for a 95% confidence interval for the mean weight gain. Report the 95% confidence interval in a sentence that explains the meaning of the 95%.

(4)Test the null hypothesis that the mean weight gain is 7.3 kilograms. Be sure to specify the null and alternative hypotheses, calculate the test statistic with degrees of freedom, and find the p-value (using R). What do you conclude?Use = 0.05.