A coffee house owner knows that customers pour different amounts of coffee into their cups. She
Samples cups from 10 costumers she believes to be representative of the customers and weighs the
Cups, finding a mean of 12.5 ounces and standard deviation of 0.5 ounces. Assuming these cups of
Coffee can be considered a random sample of all cups of coffee which of the following formulas
Gives a 95% confidence interval for the mean weight of all cups of coffee?
A) $12.5 \pm 2.228 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$
B) $12.5 \pm 2.228 \left( \frac { 0.5 } { \sqrt { 9 } } \right)$
C) $12.5 \pm 2.262 \left( \frac { 0.5 } { \sqrt { 9 } } \right)$
D) $12.5 \pm 1.969 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$
E) $12.5 \pm 2.262 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$

Question

A coffee house owner knows that customers pour different amounts of coffee into their cups. She
Samples cups from 10 costumers she believes to be representative of the customers and weighs the
Cups, finding a mean of 12.5 ounces and standard deviation of 0.5 ounces. Assuming these cups of
Coffee can be considered a random sample of all cups of coffee which of the following formulas
Gives a 95% confidence interval for the mean weight of all cups of coffee? 
A) $12.5 \pm 2.228 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$
B) $12.5 \pm 2.228 \left( \frac { 0.5 } { \sqrt { 9 } } \right)$
C) $12.5 \pm 2.262 \left( \frac { 0.5 } { \sqrt { 9 } } \right)$
D) $12.5 \pm 1.969 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$
E) $12.5 \pm 2.262 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$

Quizplus · Accepted Answer

The formula for a 95% confidence interval for the mean weight of all cups of coffee is:$ \bar{x} \pm z_{\alpha/2} \left( \frac { \sigma } { \sqrt { n } } \right)$where:$ \bar{x} $ is the sample mean$ z_{\alpha/2} $ is the z-score corresponding to the desired confidence level$ \sigma $ is the population standard deviation$ n $ is the sample sizeIn this case, we have:$ \bar{x} = 12.5 $$ z_{\alpha/2} = 2.262 $ (for a 95% confidence level)$ \sigma = 0.5 $$ n = 10 $Plugging these values into the formula, we get:$ 12.5 \pm 2.262 \left( \frac { 0.5 } { \sqrt { 10 } } \right) $Therefore, the correct answer is E.

A Coffee House Owner Knows That Customers Pour Different Amounts 12.5±2.228(0.510)12.5 \pm 2.228 \left( \frac { 0.5 } { \sqrt { 10 } } \right)12.5±2.228(10​0.5​)

A Coffee House Owner Knows That Customers Pour Different Amounts $12.5 \pm 2.228 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$