In: Statistics and Probability
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:
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