A study asked respondents, \"If ever married, how old were you when you first ma
ID: 3218421 • Letter: A
Question
A study asked respondents, "If ever married, how old were you when you first married?" The results are summarize in the MINITAB exerpt that follows complete parts (a) and (b)below. One-Sample T:AGEWED Variable N Mean SDev SE Mean 90.0% CI AGEWED 26500 22890 4.923 0.030 (22.840, 22.940) Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval x^bar = (Type an integer or a decimal) E = (Type an integer or a decimal) Interpret the confidence interval There is a 90% Probability that the mean age of people when first married is 22.890 years One can be 90% confident that the mean age of people when first married is 22.890 years a There is a 90% probability that the mean age of people when first married is between 22.840 and 22.940 years. One can be 90% confident that the mean age of people when first married is between 22.840 and 22.940 years.Explanation / Answer
Margin of Error = t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
Mean(x)=22.89
Standard deviation( sd )=4.923
Sample Size(n)=26500
Margin of Error = t a/2 * 4.923/ Sqrt ( 26500)
= 1.645 * (0.03)
= 0.05
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=22.89
Standard deviation( sd )=4.923
Sample Size(n)=26500
Confidence Interval = [ 22.89 ± t a/2 ( 4.923/ Sqrt ( 26500) ) ]
= [ 22.89 - 1.645 * (0.03) , 22.89 + 1.645 * (0.03) ]
= [ 22.84,22.94 ]
Interpretations:
1) We are 90% sure that the interval [22.84 , 22.94 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population mean
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