How much money does the average professional football fan spend on food at a single football game? That question was posed to ten randomly selected football fans. The sampled results show
That the sample mean and sample standard deviation were $70.00 and $17.50, respectively. Use
This information to create a 95 percent confidence interval for the population mean.
A) $70 \pm 1.833 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$
B) $70 \pm 2.262 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$
C) $70 \pm 2.228 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$
D) $70 \pm 1.960 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$

Question

How much money does the average professional football fan spend on food at a single football game? That question was posed to ten randomly selected football fans. The sampled results show
That the sample mean and sample standard deviation were $70.00 and $17.50, respectively. Use
This information to create a 95 percent confidence interval for the population mean. 
A) $70 \pm 1.833 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$
B) $70 \pm 2.262 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$
C) $70 \pm 2.228 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$
D) $70 \pm 1.960 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$

Quizplus · Accepted Answer

The correct choice is B because it uses the t-distribution critical value for a 95% confidence interval with 9 degrees of freedom (n-1, where n is the sample size of 10). The value 2.262 is the appropriate t-score for a 95% confidence level with 9 degrees of freedom. Choices A, C, and D use incorrect critical values for this scenario.

How Much Money Does the Average Professional Football Fan Spend 70±1.833(17.5060)70 \pm 1.833 \left( \frac { 17.50 } { \sqrt { 60 } } \right)70±1.833(60​17.50​)

How Much Money Does the Average Professional Football Fan Spend $70 \pm 1.833 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$