Question

Question 3: Suppose the height for girls is distributed normally with a mean (μ₁) of 66 inches and a standard deviation of 3.5 inches. The height for boys is distributed normally with a mean (μ₂) of 68 inches and a standard deviation of 4 inches.

a) Using R, simulate a sample of n₁ = 50 boys and n₂ = 50 girls and compute ?̅₁ − ?̅₂. Repeat 5,000 times. Plot the histogram of the sampling distribution of ?̅₁ − ?̅₂.

b) Estimate Var(?̅₁ − ?̅₂) based on the results of your simulation. Does this match the expected variance of ?̅₁ − ?̅₂?

c) Compute a 95% confidence interval for the difference of the means (μ₁ - μ₂). What percentage of the time does the 95% confidence interval contain the true difference in (μ₁ - μ₂) of -2? Assume unequal variances.

d) Compute a 95% confidence interval for the difference of the means (μ₁ - μ₂). What percentage of the time does the 95% confidence interval contain the true difference in (μ₁ - μ₂) of -2? Assume equal variances.

e) Compare your results in (c) and (d).

Answer 1

Need R code is given below