Question

A researcher is interested in knowing the average height of the women in a village. To the researcher, the population of interest is the in the village, the relevant population data are the in the village, and the population parameter of interest is the . There are 480 women in the village, and the sum of their heights is 2,620.8 feet. Their average height is feet. Instead of measuring the heights of all the village women, the researcher measured the heights of 20 village women and calculated the average to estimate the average height of all the village women. The sample for his estimation is , the relevant sample data are the , and the sample statistic is the . If the sum of the heights of the 20 village women is 102 feet, their average height is feet.

Answer 1

Answer:

$\mu = \frac{2620.8}{480}= 5.46$

$\bar X = \frac{102}{20}= 5.1$

See explanation below.

Step-by-step explanation:

Let X the random variable who represent the height of the women in a village

N= 480 that represent the population size of all the women in the village

$\sum_{i=1}^N X_i = 2620.8 ft$

For this case if we want to calculate the population mean we can use the following formula:

$\mu = \frac{\sum_{i=1}^n X_i}{N}$

And replacing we got: $\mu = \frac{2620.8}{480}= 5.46$

For this case this value represent a parameter since is the information with all the population of interest

For the sample we have the following data:

n = 20 represent the sample size selected for the researcher

$\sum_{i=1}^N X_i = 102 ft$

And we can calculate the sample mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got: $\bar X = \frac{102}{20}= 5.1$

And for this case this value represent an statistic since is calculated from the info obtained with the sample selected.