A random sample of 64 middle-aged people 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.
Please show all work.