Salary information regarding male and female employees of a...

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) 44 41 Population Variance (?^2) 128 72 If you are interested in testing whether or not the population average salary of males is significantly greater than that of females, at ? = .05, the conclusion is that the population a. average salary of males is greater than females cannot be proved. b. average salary of males is significantly greater than females. c. average salary of males is significantly lower than females. d. salaries of males and females are equal.

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00:01 Okay, so i see that you need help with this question and it says salary information regarding male and female employees of a large company is shown below so i took the liberty of putting this in a table and it's giving the population variance if you are interested in testing whether or not the average salary of males or whether or not the average salary of males is significantly greater than females using a 5 % level of significance the conclusion is question options the average salary of males is significantly greater than females the average salary of males is significantly lower than females the average salary of males and females are equal do not reject ho okay, so what i'm going to do is i'm going to find the confidence interval of both so i'm going to calculate the population standard deviation so i'm gonna find the square root of 128 and that is 11 .3 i'm just gonna round to the nearest tens place and the square root of 72 is 8 .5 so for the confidence interval of the average of male so 64 is the sample size and 44 is the average and the sample standard deviation is 11 .3 and i'm gonna go out two decimal places with a 95 % confidence interval so using the normal distribution sample this standard population standard deviation of 11 .3, so the i'm going to do 44 plus or minus 1 .96 times 11 .3 divided by the square root of 64 so that's 44 plus or minus 2 .77 and so that is a confidence interval of 41 .23 to 46 .77 then as far as females go they make on average $41 ,000 a year with a sample size of 36 and a population standard deviation of 8 .5 and there's if you do 41 plus or minus 1 .96 times 8 .5 over the square root of 36 that's 41 plus or minus 2 .78 so then that would be a confidence interval of 38 point 22 comma 43 point 78 so we can say that the average salary of males c is significantly greater than females the average okay, so the average salary of males is significantly greater than females if we were to compare the two the difference between the two means then i would do so we have equal variances if i use a normal distribution the averages are 44 and 41 population standard deviation is 11 .3 and 8 .5 sample standard deviation sample size is 64 and 36 and let's calculate that so the difference between the means if i was to do the confidence interval it would be negative 0 .9 to 1 comma 6 .9 to 1 and so that the standard of error would be 2 .005 and for a normal distribution, so there is a significant difference...

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