Independent random samples of professional football and basketball players gave
ID: 3220655 • Letter: I
Question
Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players: x1; n1 = 21
Weights (in lb) of pro basketball players: x2; n2 = 19
(a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to one decimal place.)
(b) Let 1 be the population mean for x1 and let 2 be the population mean for x2. Find a 99% confidence interval for
1 2. (Round your answers to one decimal place.)
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.
(a) If no preliminary sample is taken to estimate p, how large a sample is necessary to be 95% sure that a point estimate p will be within a distance of 0.12 from p? (Round your answer up to the nearest whole number.)
small businesses
(b) In a preliminary random sample of 30 small businesses, it was found that twelve had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 95% sure that a point estimate p will be within a distance of 0.120 from p? (Round your answer up to the nearest whole number.)
more small businesses
Explanation / Answer
Solution:
a)
n1 = 21
n2 = 19
x1 = 259.6
s1 = 12.2
x2 = 205.8
s2 =13.04
b) Mean difference = x1-x2 = 53.8
Std error for difference = sqrt( (s1^2/n1)+(s2^2/n2))
= sqrt((12.2^2/ 21)+(13.04^2/19)) = 4.0046
99% z value = 2.58
Margin of error = ±(2.58)4.0046=±10.3318
Confidence interval lower bound = 53.8-10.3318 = 43.4682
Upper bound = 53.8+10.3318 = 64.1318