Question

A simple random sample of 5 months of sales data provided the following information: Month: 1 2 3 4 5 Units Sold: 94 105 85 94 92 (a) Develop a point estimate of the population mean number of units sold per month. x = (b) Develop a point estimate of the population standard deviation. If required, round your answer to two decimal places. s =

Answer 1

Answer:

a) x = 94 units/month

b) s = 51.50 units/month

Step-by-step explanation:

The adequate point estimation of the population mean and standard deviation are the sample mean and sample standard deviation.

a) Point estimation of the population (sample mean)

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(94+105+85+94+92)\\\\\\M=\dfrac{470}{5}\\\\\\M=94$

b) Point estimation of the population standard deviation (sample standard deviation)

$s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{4}((94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2)\\\\\\s=\dfrac{206}{4}\\\\\\s=51.50$

Answer 2

Using statistical concepts, it is found that:

a) The point estimate for the population mean is of: $\overline{x} = 94$

b) The point estimate for the population standard deviation is of: $s = 7.18$

Item a:

• The mean of a data-set is the sum of all observations in the data-set divided by the number of observations.

• The point estimate for the population mean is the sample mean.

In this problem, the sample is: 94, 105, 85, 94, 92.

Thus, the mean is:

$\overline{x} = \frac{94 + 105 + 85 + 94 + 92}{5} = 94$

Item b:

• The standard deviation of a data-set is the square root of the sum of the differences squared between each observation and the mean, divided by one less than the number of values.

• The point estimate for the population standard deviation is the sample standard deviation.

Then:

$s = \sqrt{\frac{(94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2}{4}} = 7.18$

A similar problem is given at https://brainly.com/question/13451786