It is claimed that 10 year old boys and girls both have the same average height (52 inches). A researcher studies 65 boys and finds that their average height is 52.8 with a variance of 98. The 111 girls in the study had an average height of 54.1 with a variance of 123. Construct a 95% confidence interval for the difference in the heights of 10 year old boys and girls based on these samples. Does the confidence interval support the claim that 10 year old boys and girls have the same average height?

Step-by-step explanation:

Let us calculate std dev and std error of two samples

Sample N Mean Std dev Std error

1 65 52.8 9.9 1.22279

2 111 54.1 11.09 1.0526

Assuming equal variances

df = 111+65-2=174

Pooled std deviation = combined std deviation = 10.6677

Pooled std error = 10.6677/sqrt 174 = 0.808

difference in means = 52.8-54.1 = - 1.3

Margin of error = 0.5923

(t critical 1.6660)

Confidence interval

= (-4.4923, 1.8923)

Since 0 lies in this interval we can accept null hypothesis that 10 year old boys and girls have the same average height