The age at first marriage is found for a random sample of n = 81 women who graduated from college in 1980. The mean age is  = 25.5, and the standard deviation is s = 4.5 years. a. Find the value of...

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The age at first marriage is found for a random sample of n = 81 women who graduated from college in 1980. The mean age is
 = 25.5, and the standard deviation is s = 4.5 years.


a. Find the value of the standard error of the sample mean. Write a sentence that interprets this value. (Refer to Section 11.1 for guidance.)


b. Find a 95% confidence interval for the population mean.


c. Write a sentence that interprets the confidence interval in the context of this situation.




Answered Same DayDec 25, 2021

Answer To: The age at first marriage is found for a random sample of n = 81 women who graduated from college in...

David answered on Dec 25 2021
116 Votes
a)
Estimated Standard Error of Sample mean:
SEX =
s√
n
= 4.5√
81
= 0.5
This is the expected difference between sample mean and true mean
b)
95% CI for µ using t-dist
Sample Mean = x = 25.5
Sample Standard deviation = s = 4.5
Sample Size = n = 81
Significance level = α = 1− 0.95 = 0.05
Degrees of freedom for t-distribution, d.f . = n− 1 = 80
Critical Value = tα/2,df = t0.025,df=80 = 1.990 (from t-table, two-tails, d.f . = 80
)
Margin of Error = E = tα/2,df...
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