please answer in mathematical details with explanation, you can use Excel but plz refer to that in the spreadsheet with formulas , plz also include interpretation for the answer

1- A health organization are investigating the efficacy of a diet plan designed to increase the caloric intake of elderly people. The increase in daily caloric intake in the following sample of individuals who are put on the plan is (a minus sign signifies that calories consumed went down):

121 188 284 -102 -94 259 226 183 152 312 167

Construct and interpret a 99% confidence interval for the mean increase in caloric intake forall people who are put on this diet,

rounds to the nearest calorie.

2- The amount of a particular biochemical substance related to bone breakdown was measured in 30 healthy women. The sample mean was 3.3 nanograms per milliliter (ng/mL). Assuming a population standard deviation of 1.4 ng/mL, construct and interpret an 80% confidence interval for the mean level of this substance in all healthy women.

3- A real estate agent wishes to estimate, to within $2.50, the average retail cost per square foot of newly built homes, with 95% confidence. Assuming that the population standard deviation of such costs is $10.00, estimate the size sample required.