Question

In: Statistics and Probability

1. Beth wants to determine a 95 percent confidence interval for the true proportion of high...

1. Beth wants to determine a 95 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. How large of a sample must she have to get a margin of error less than 0.02?

HINT: To find n, since no previous study has been done, use the value p = 0.5 for the proportion and one of the values (1.282, 1.645, 1.96, 2.576) for the critical value depending on the confidence level. Don't forget to round your value of n up.

2. An SRS of size 28 is drawn from a population that has a normal distribution. The sample has a mean of 118.5 and a standard deviation of 7.

Give the standard error of the mean:

Solutions

Expert Solution

Solution :

Given that,

= 0.5

1 - = 0.5  

margin of error = E = 0.02

1)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= (1.96 / 0.02)2 * 0.5 * 0.5

= 2401

sample size = 2401

2)

mean = = 118.5

standard deviation = s = 7

n = 28

= = 118.5

standard error of the mean:

s = s / n = 7 / 28 = 1.3229


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