The standard deviation for the number of times per year single people go on date
ID: 3172473 • Letter: T
Question
The standard deviation for the number of times per year single people go on date is known to be 18.3. You are interested in finding a 95% confidence interval for the average dates per year that single college students go on. The data below show the results of the survey that you took. Assume the standard deviation for single college students is the same as the standard deviation for single people in general.
5,8,12,45,0,23,17,4,6,9,16
Assume a normal distribution and round your answers to two decimal places.
A. The sampling distribution follows a distribution.
B. With 95% confidence the mean number of dates that single college students have each year is between and .
C. If many groups of 11 randomly selected single college students are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean dates per year and about percent will not contain the true population mean dates per year.
Explanation / Answer
The 95% c.i=xbar+-t(s/sqrt n), where, xbar is sample mean, t is t critical at alpha/2, and df=n-1, s denotes sample standard deviation, and n is sample size. The computational formula for xbar=sigma x/n, s=sqrt[1/n-1 sigma (x-xbar)^2].
=14.09+-2.228(12.41/sqrt 11)
=5.75, 22.43
A. It is given that population is normally distributed, and the sample size is less than 15, therefore, the sampling distribution follows a t distribution.
B. The lower and upper limit of 95% c.i (computed above) is 5.75 and 22.43.
C. The 95% confidence interval means that with repeated samples taken from same population and confidence interval is computed for each sample, then 95% of the confidence intervals will contain the true population mean dates per year.
95%, 5%.
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