Question

The PLNU student-athletes on the women's teams compete in various NCAA-II sports. Each team may be regarded as a random sample of all the NCAA-II athletes in that sport. The 14 players listed on the roster for the 2010-11 Women’s Basketball team had an average height of 69.76 inches with a standard deviation of 2.80 inches. Give a 90% confidence interval for the average height of NCAA-II women’s basketball players in that year. Write a one or two sentence summary in non-statistical language to describe what you have found, not how you found it. Your audience is people who have never had a statistics class (think of middle of the road 8th graders, not the really bright ones).

Answer 1

Given that,

= 69.76

s =2.80

n = 14

Degrees of freedom = df = n - 1 = 14- 1 = 13

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,13 = 1.771 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 1.771* ( 2.80/ 14) = 1.3253

The 90% confidence interval estimate of the mean is,

- E < < + E

69.76 -1.3253 < < 69.76+ 1.3253

68.4347< < 71.0853

( 68.4347, 71.0853)

The 90% confidence interval estimate of the mean is,( 68.4347, 71.0853)