Question

1. You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. Your would like to be 99.9% confident that you estimate is within 4% of the true population proportion. How large of a sample size is required? n =

2. A regression analysis was performed to determine if there is a relationship between hours of TV watched per day (xx) and number of sit ups a person can do (yy). The results of the regression were:

y=ax+b
a=-0.671
b=23.519
r2=0.537289
r=-0.733

Use this to predict the number of sit ups a person who watches 2.5 hours of TV can do, and please round your answer to a whole number.

3. Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as

y=−37.77x+67.23 and the r=-0.449.

What proportion of the variation in y can be explained by the variation in the values of x?
r² = %

Answer 1

1)

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 0.04

Z_/2 = 3.29

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (3.29 / 0.04)² * 0.5 * 0.5

= 1692

sample size = n = 1692

2)

y = -0.671 + 23.519 * 2.5 = 58

Number = 58

3)

r ²= (-0.449) ² = 0.2016 = 20.16%