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Having a cholesterol level above 200 mg/dL is a definite cause for concern. Do women have more reason to be concerned than men?

On average, men's cholesterol level is 191 mg/dL with a standard deviation of 46 mg/dL. For women, the average is 196 mg/dL with a standard deviation of 44 mg/dL.

A computer randomly selects the medical records of 30 men and 30 women and calculates the difference of the average cholesterol level of the two genders. This process is repeated many times.

What is the standard deviation of the sampling distribution of the difference of the mean cholesterol levels for men and women?

A

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\sqrt { { 46 }^{ 2 }+{ 44 }^{ 2 } }$

B

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\sqrt { \frac { 46 }{ 30 } +\frac { 44 }{ 30 } }$

C

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\sqrt { \frac { { 46 }^{ 2 } }{ 30 } +\frac { { 44 }^{ 2 } }{ 30 } }$

D

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\frac { \sqrt { { 46 }^{ 2 }+{ 44 }^{ 2 } } }{ 30 }$

E

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\sqrt { \frac { { 46 }^{ 2 } }{ 30 } } +\sqrt { \frac { { 44 }^{ 2 } }{ 30 } }$

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