Question

The average expenditure on Valentine's Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 30 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20.a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?

Answer 1

Answer:

The point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is $67.03.

Step-by-step explanation:

In statistic, point estimation comprises of the use of sample data to estimate a distinct data value (known as a point estimate) which is to function as a "best guess" or "best estimate" of an unidentified population parameter.  

The point estimate of the population mean (µ) is the sample mean ($\bar x$).

The point estimates are always computed using the sample data.

So for the point estimates to be the best estimate of a parameter the sample taken from the population must large enough, i.e. n ≥ 30.

In this case, the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is to be determined.

The point estimate for the difference between two population mean is given by the difference between two sample means.

The information provided is:

$n_{M}=40\\n_{F}=30\\\bar x_{M}=\ 135.67\\\bar x_{F}=\ 68.64$

The sample sizes are large enough.

Compute the point estimate for the difference between two population mean as follows:

$E(\mu_{M}-\mu_{F})=\bar x_{M}-\bar x_{F}=135.67-68.64=67.03$

Thus, the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is $67.03.