A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups.Suppose the distribution of the population of number of pushups that can be done is approximately normal. If we would like to capture the population mean with 95% confidence the margin of error would be ??
A) $1.960 \left( \frac { 9 } { \sqrt { 10 } } \right)$
B)? $2.125 \left( \frac { 15 } { \sqrt { 10 } } \right)$
C)? $2.262 \left( \frac { 9 } { \sqrt { 10 } } \right)$
D)? $3.250 \left( \frac { 15 } { \sqrt { 10 } } \right)$

Question

Quizplus · Accepted Answer

The margin of error for a 95% confidence interval when the sample size is small (n < 30) and the population standard deviation is unknown is calculated using the t-distribution. With 9 degrees of freedom (n-1), the t-value is approximately 2.262. Therefore, the margin of error is $2.262 \left( \frac { 9 } { \sqrt { 10 } } \right)$.

A Statistics Teacher Started Class One Day by Drawing the Names