Answer :
Answer:
With 95% confidence the true difference in mean annual cost of attending private and public colleges is between 14.488 and 26.251.
Step-by-step explanation:
To conduct a confidence interval on a difference in mean, we first must have the mean and standard deviation of both sample populations.
Calculating both,
- Private college mean (x) : 42.73
- Private college standard deviation (s): 7.08
- Public college mean (x) : 22.36
- Public college standard deviation (s): 4.58
The general formula for a confidence interval for a difference in mean is
[tex]\rm (\bar x_2- \bar x_1) \pm t^*(Standard~Error)[/tex]
[tex]\rm (\bar x_2- \bar x_1) \pm t^*\left(\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2} } \right)[/tex]
To find t* we find the degrees of freedom (df). To do that we
- take the smaller sample size of the two given and subtract 1 from it.
- On a t-table we find the df value (if it's not there then round down to the nearest number on the df column) and the confidence level and the correlating cell is the t* value.
The smaller sample is 10 so the df is 9, so the t* value is 2.262.
Plugging in all the values we know we get a confidence interval of
[tex]\rm (42.73- 22.36) \pm (2.262)\left(\sqrt{\dfrac{7.08^2}{10}+\dfrac{4.58^2}{12} } \right)[/tex]
[tex]=(14.488,26.251)[/tex]
With 95% confidence the true difference in mean annual cost of attending private and public colleges is between 14.488 and 26.251.
