Question

1. Confidence Intervals: (20 pts)
   For this exercise, use the dataset titled “Protein and Weight Gain”
   

Generate summary statistics for the weight gain by protein source.


Statistics

Variable	source	Total Count	Mean	StDev
weight_gain	beef	20	89.60	17.71
	cereal	20	84.90	14.99
	pork	20	89.10	17.32

1. 
   
   
   
2. Estimate a 95% confidence interval for the weight gain with beef as a source. Use a t-statistic value based on the n for beef, given from the table below (use the closest value). (Note: we’ve been using 1.96, you’ll be using t=2.093)
   
   
   
   
   
   
   
   
3. Estimate a 95% confidence interval for the weight gain with cereal as a source. Use a t-statistic value based on the n for beef, given from the table below (use the closest value). (Note: we’ve been using 1.96, you’ll be using t=2.093)
   
   
   
   
   
   
   

Estimate a 95% confidence interval for the weight gain with pork as a source. Use a t-statistic value based on the n for beef, given from the table below (use the closest value). (Note: we’ve been using 1.96, you’ll be using t=2.093)

Answer 1

The degrees of freedom (df) = n – 1 = 20 – 1 =19

At the significance level 0.05 and the degrees of freedom 19, the two-sided critical value obtained from the t-table is +/- 2.093.

(A).

The 95% confidence interval for the weight gain with beef as a source is,

Thus, the required interval is (81.3116, 97.8884).

(B).

The 95% confidence interval for the weight gain with cereal as a source is,

Thus, the required interval is (77.8845, 91.9155).

(C).

The 95% confidence interval for the weight gain with pork as a source is,

Thus, the required interval is (80.9941, 97.2059).