Question 1201105: Ibrahim Masood recently assumed the position of director of the national club of south valley. he would like some current data on how long current members of club have been members. To investigate, suppose he selects a random sample of 40 current members. The mean length of membership for the sample is 8.32 years and the standard deviation is 3.07 years.
Develop a 90% confidence interval for the population mean.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sample mean is 8.32 years
population standard deviation is 3.07 years.
z-score formula is z = (x-m)/s
z is the z-score
x is the upper and lower limit of the sample mean
x is the sample mean
s is the standard error
standard error = sample standard deviation / squre root of sample size = 3.07 / sqrt(40) = .4854096208.
t-score is indicated because the mean is taken from the sample, rather than from the population.
critical t-score with 39 degrees of freedom (sample size minus 1) is equal to 1.684875066.
t-score formula is t = (x-m)/s
t is the t-score
x is the estimated upper and lower limits of the population inferred from this sample based on the critical t-scores.
m is the smaple mean.
s is the standard error that is calculated from the sample standard deviation divided by the squre root of the sample size.
for the upper limit, the t-score formula becomes:
1.684875066 = (x - 8.32) / .4854096208
solve for x to get:
x = 1.684875066 * .4854096208 + 8.32 = 9.137854567.
for the lower limit, the t-score formula becomes:
-1.684875066 = (x - 8.32) / .4854096208
solve for x to get:
x = -1.684875066 * .4854096208 + 8.32 = 7.502145433.
your 90% confidence interval for how long current members of the national club of south valley have been members, calculated from the t-score, is 7.502145433 to 9.137854567 years.
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