Question

Chloe would like to know if phone use at her college is unusual or not. Since this question is too broad she decides to compare phone usage at her college and at TSU college. Chloe samples 17 students at her college and finds the average phone usage is 1.9 hours per day with standard deviation 1.2 hours. Her friend Tracy at TSU college does a similar random survey of 28 students and finds an average phone usage to be 1.7 hours per day with standard deviation 0.9 hours. a. Compute the standard error (SE).

b. Compute the margin of error (ME) for a 95% confidence interval.

c. What is the 95% confidence interval for the difference of the means?

d. Interpret the confidence interval you found in the previous part in context.

Answer 1

The provided sample means are shown below:

Xˉ1​=1.9 and Xˉ2​=1.7

Also, the provided sample standard deviations are:

s1​=1.2 and s2​=0.9

and the sample sizes are n1​=17 and n2​=28.

a) Standard error of mean of difference of means

S.E=

b) Degrees of freedom is 26.933= 27

t critical value= 2.052 at alpha=0.05

Margin of error= t critical* S.E

= 2.052*0.3371

= 0.6917

c) 95% confidence interval is

The 95% confidence interval is −0.492<μ1​−μ2​<0.892.

d) Since 95% confidence interval does contain true population mean difference zero therefore NOT significant. From confidence interval we can not conclude that if phone use at her college is unusual or not.​