Question

please answer with showing the work with excel functions

3.) Salary Offers A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. The sample will be used to obtain a 99% confidence interval for the mean salary offer. a.) The critical value to use in obtaining the confidence interval is ANSWER: b.) The confidence interval goes from ANSWER: c.) Interpret the confidence interval.

Answer 1

Answer)

Excel function to find margin of error is

CONFIDENCE.T( alpha, standard_dev, size )

So, first we need to find the mean and s.d of the given data

Mean = (sum of the observations)/number of observations

Mean = (48 + 51....)/10 = 49.9

To find s.d first we need to subtract mean from each and every observation and then we need to take the square and finally add them

(48-49.9)^2 + (51-49.9)^2...

= 128.9

S.d = √{128.9/(10-1)} = 3.7845

Degrees of freedom is = n-1 = 9

For 9 degrees of freedom and 99% confidence level, critical value t from t table is = 3.25

Margin of error (MOE) = t*s.d/√n = 3.25*3.7845/√10 = 3.889

Confidence interval is given by

(Mean - MOE, Mean + MOE)

(46.011, 53.789)

We are 99% confident that true population mean lies in this estimated interval

Throgh excel

Function for margin of error is

CONFIDENCE.T( alpha, standard_dev, size )

Alpha = 1- confidence level = 1 - 0.99 = 0.01

S.d = 3.7845

Size = 10

=CONFIDENCE.T( 0.01, 3.7845, 10 )

Answer would be 3.889

Then find the interval

(Mean - MOE, Mean + MOE)