1 Nutritionists stress that weight control generally requires significant reductions in the intake of fat. A random sample of 64 middle-aged men on weight control programs is selected to determine whether their mean intake of fat exceeds the recommended 30 grams per day. The sample mean and standard deviation are 37 and 32 respectively.
(a) Construct a 95% confidence interval for the mean.
(b) At a 5% level of significance can you conclude that the true mean intake of fat exceeds 30 grams   per day? Find also the P-value.
2。The costs associated with conducting interviews for a job opening have skyrocketed over the years. According to a Harris interactive survey, 211 of 502 senior human resources executives at U.S companies believe that their hiring managers are interviewing too many people to find qualified candidates for the job. Suppose the true proportion of human resource executives who believe that their hiring managers are interviewing too many people is given by p.
(a) Construct a 90% confidence interval for the true mean proportion p.
(b) At a 5% level of significance, can you conclude that the true proportion p is more than 40%? Find also the P-Value.