A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 Squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 Grams and standard deviation of 1.88gm. Assuming these squirrels can be considered a random Sample of all red squirrels which of the following formulas gives a 95% confidence interval for the Mean weight of all squirrels?
A) $12.32 \pm 2.262 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$
B) $12.32 \pm 2.228 \left( \frac { 1.88 } { \sqrt { 9 } } \right)$
C) $12.32 \pm 2.262 \left( \frac { 1.88 } { \sqrt { 9 } } \right)$
D) $12.32 \pm 2.228 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$
E) $12.32 \pm 1.96 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$

Question

A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 Squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 Grams and standard deviation of 1.88gm. Assuming these squirrels can be considered a random Sample of all red squirrels which of the following formulas gives a 95% confidence interval for the Mean weight of all squirrels? 
A) $12.32 \pm 2.262 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$
B) $12.32 \pm 2.228 \left( \frac { 1.88 } { \sqrt { 9 } } \right)$
C) $12.32 \pm 2.262 \left( \frac { 1.88 } { \sqrt { 9 } } \right)$
D) $12.32 \pm 2.228 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$
E) $12.32 \pm 1.96 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$

Quizplus · Accepted Answer

The formula for a 95% confidence interval for the mean is:mean +/- z-score * (standard deviation / square root of sample size)where the z-score for a 95% confidence interval is 1.96.Plugging in the given values, we get:12.32 +/- 1.96 * (1.88 / square root of 10)which simplifies to:12.32 +/- 2.262 * (1.88 / 3.162)which further simplifies to:12.32 +/- 2.262 * 0.594which gives us a confidence interval of:12.32 +/- 1.34Therefore, the correct answer is A.

A Wildlife Biologist Wants to Determine the Mean Weight of Adult