Question

17

Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 5% at the 95% confidence level, how many randomly selected teenagers must we survey?

18

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=61%. You would like to be 95% confident that your esimate is within 3% of the true population proportion. How large of a sample size is required?

n =

32

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=78.78x+19.44

and the r=0.09.

What percentage of the variation in y can be explained by the variation in the values of x?
r² = % (Report exact answer, and do not enter the % sign)

Answer 1

Solution:

17 Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 5% at the 95% confidence level, how many randomly selected teenagers must we survey?

Answer:

Where:

is the critical value at the 0.05 significance level.

Therefore, we have:

18. You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=61%. You would like to be 95% confident that your estimate is within 3% of the true population proportion. How large of sample size is required?

Answer:

Where:

is the critical value at the 0.05 significance level.

Therefore, we have:

32. 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=78.78x+19.44

and r=0.09.

What percentage of the variation in y can be explained by the variation in the values of x?
r² = % (Report exact answer, and do not enter the % sign)