Question

You are interested in finding a 98% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 12 randomly selected non-residential college students. Round answers to 3 decimal places where possible. 27 6 19 11 7 11 14 14 22 11 17 5.

a. To compute the confidence interval use a distribution.
b. With 98% confidence the population mean commute for non-residential college students is between and miles.
c. If many groups of 12 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About 98 percent of these confidence intervals will contain the true population mean number of commute miles and about percent will not contain the true population mean number of commute miles.

Answer 1

t distribution, two percent

Explanation:

From the sample of 12 entries we find that

Mean 12.83333333

Standard Error 2.187545093

Median 12.5

Mode 11

Standard Deviation 7.577878491

Sample Variance 57.42424242

Kurtosis -0.410024213

Skewness 0.314845048

Range 26

Minimum 1

Maximum 27

Sum 154

Count 12

Confidence Level(98.0%) 6.794

a) Because sample size is less than 30 and population std dev is not known we use t distribution

b) 98% confidence interval margin of error = 6.794

Hence confidence interal =
`(12.833-6.794, 12.833+6.794)\\=( 6.039,19.627)`

c) About 98 percent of these confidence intervals will contain the true population mean number of commute miles and about two percent will not contain the true population mean number of commute miles.