Question

A study is done to see if the brand of someone’s phone is related to how many minutes of call time they use per month. The data can be found in the Excel sheet labeled Q2 Data. There were 34 people studied and their phone brand and number of minutes were recorded.

a.     Use ToolPak to run a t-Test and summarize the information found in the table below. You should also print the excel output.

	Samsung	Apple
Sample Mean
Sample Variance
Number of Observations

b.     The point estimate for the difference in means of Samsung-Apple is:

c.     Find the standard error for this estimate. Write the general formula first.

d.     Find the Confidence Interval for the difference in means of Samsung - Apple. Write the general formula first.

95% CI for  

e.     Based on your confidence interval, would you conclude that each phone brand has the same number of mean call minutes used per month? Why?

f.      Now perform a hypothesis test using the information you have already found to test if the mean call minutes of the two phone brands are equal.

                                 i.        State the null and alternative hypothesis being tested.

                               ii.        Give the t Stat and corresponding p-value. Would you conclude that the phone brands have the same mean call minutes?

Phone	Used Minutes
Samsung	14.1
Samsung	17.8
Samsung	21.0
Samsung	6.6
Samsung	47.1
Samsung	15.5
Samsung	15.7
Samsung	66.3
Samsung	36.2
Samsung	7.8
Samsung	67.1
Samsung	40.6
Samsung	62.8
Samsung	51.1
Samsung	46.7
Samsung	29.8
Samsung	63.7
Apple	76.4
Apple	92.3
Apple	65.1
Apple	52.5
Apple	88.8
Apple	29.5
Apple	50.6
Apple	15.0
Apple	47.9
Apple	98.9
Apple	96.5
Apple	21.3
Apple	22.6
Apple	24.3
Apple	93.3
Apple	27.3
Apple	28.3

Answer 1

Following is the output of t test:

(a)

Following is the completed table:

	Samsung	Apple
Sample Mean	35.876	54.741
Sample Variance	463.982	946.456
Number of Observations	17	17

(b)

The estimate for the difference in means of Samsung-Apple is:

(c)

The standard error of estimate:

SE = 9.1086

(d)

Degree of freedom for t is df=32, so t-critical value is 2.0369. So required confidence interval for   will be

(e)

No we cannot conclude that each phone brand has the same number of mean call minutes used per month because confidence interval does not contain zero.

(f)

(i)

Hypotheses are:

(ii)

The test statistics is

t = -2.07

The p-value is: 0.0465

Since p-value is less than 0.05 so we reject the null hypothesis. You would conclude that the phone brands have the same mean call minutes.