Question

Salary information regarding male and female employees of a large company is shown below. male female sample size 64 36 sample mean salary (in $1000) 45 41 population variance () 128 72 ​ the standard error of the difference between the two sample means is question 2 options:

a) 2.0.
b) 7.46.
c) 4.24.
d) 4.

Answer 1

The standard error of the difference between two independent sample means, given the population variances and sample sizes for male and female employees, is calculated using a specific formula and is found to be 2.0.

Step-by-step explanation:

The question is asking to compute the standard error of the difference between two sample means, given the sample sizes, mean salaries, and population variances of male and female employees at a large company. The formula to calculate the standard error of the mean difference between two independent samples is:

SE = √[(s1²/n1) + (s2²/n2)]

where s1² and s2² are the population variances, and n1 and n2 are the sample sizes for the two groups. Here, for male employees (group 1), we have a population variance s1² = 128 and sample size n1 = 64. For female employees (group 2), we have population variance s2² = 72 and sample size n2 = 36.

Plugging in the values:

SE = √[(128/64) + (72/36)]
SE = √[(2) + (2)]
SE = √[4]
SE = 2.0

Therefore, the standard error of the difference between the two sample means is 2.0.