Answer to Question #327204 in Statistics and Probability for Roy

Question

Form a group of five students or five members of your Family. Get the height (in cm) of each member of the group. Use the properties in solving for the mean , variance and standard deviation of sampling distribution of the sample means.

a. Compute the population mean.

b. Complete the population variance.

c. Find the population standard deviation.

d. List all possible samples of size 2 which can be drawn with replacement and their corresponding means.

e. Construct the sampling distribution of the sample means.

f. Find the mean of the sampling distribution of means.

g. Find the mean of the sampling distribution of means.

h. Find the standard deviation of the sampling distribution.

Answer 1

$The\,\,heights\,\,are:\\196,178,171,164,118\\a:\\\mu =\frac{196+178+171+164+118}{5}=165.4\\b:\\\sigma ^2=\frac{\left( 196-165.4 \right) ^2+\left( 178-165.4 \right) ^2+\left( 171-165.4 \right) ^2+\left( 164-165.4 \right) ^2+\left( 118-165.4 \right) ^2}{5}=675.04\\c:\\\sigma =\sqrt{\sigma ^2}=\sqrt{675.04}=25.9815\\f:\\\mu _{\bar{x}}=\mu =165.4\\g:\\the\,\,same\\h:\\\sigma _{\bar{x}}=\sqrt{\frac{N-n}{n\left( N-1 \right)}}\sigma =\sqrt{\frac{5-2}{2\left( 5-1 \right)}}\cdot 25.9815=15.9104$