# Thread: help with "statistical inferance about means and proportions with two populations"

1. ## help with "statistical inferance about means and proportions with two populations"

Howdy, Last week i was rather ill and missed a couple days of class. I've been behind ever since and dispite my efforts to catch up can't make sense of most of the lectures since then. I have a test on Friday and have been banging my head against a desk for the past three hours in the library trying to make sense of these questions. I have the answers, I just have no idea how to get them. I have a big list of formulas for this chapter most of which i do not understand and have tried plugging the various numbers in but with no success. Any help or explanation on how to do this would be greatly appreciated, thank you

Male Female
sample size 64 36
Sample mean Salary (in 1k\$) 44 41
Population Variance 128 72

The P value is...
The Standard error for the difference between the two means is...
The point estimate of the difference between the means of the two populations is...
at 95% confidence, the margin of error is...
The 95% confidence interval for the difference between the means of the two populations is...
if you are interested in testing whether or not the average salary of males is significantly greater than that of females the test statistic is...

Again any explanation on how to solve any of these problems is greatly appreciated. Thank you for your time
chris

2. It looks like this problem is about the difference in means. You can compare men vs women, without having the individual data--you just need the mean and variance/standard deviation and sample size.

Let's take the difference to be men - women (it could just as well be women - men). Obviously, everyone can see that the mean difference is 44000 - 41000 = 3000. This is the point estimate; sometimes statistics makes sense.

Often, we can assume that data values are normally distributed--since all they're giving us is the data summary, then let's just go with that assumption. Then the margin of error is proportional to the standard error. Usually they will ask you to calculate the margin of error at the 95&#37; level of confidence.

At 95% level of confidence, margin of error = 1.96 * standard error
At 90% level of confidence, margin of error = 1.645 * standard error
and so on.
As you allow a larger margin of error, you level of confidence in your estimate increases (this should also be pretty clear). Those "proportionality constants" 1.645, 1.96, etc are near and dear to our hearts--you'll soon have them memorized too.

Once you've got that, then the 95% confidence interval for the difference = point estimate +/- margin of error, eg 3000 +/- 200. This is sometimes written in interval notation as [2800, 3200].

(I am just giving numbers as an example, but the idea remains the same) This means that we are 95% confident that the difference between men and women is between +2800 and +3200; we say that the average salary of males is significantly greater than that of females. Even if the confidence interval was between +50 and +70, that would be considered a statistically significant difference.

The test statistic = point estimate / margin of error.

ps It looks strange that the first question is about p-value; unless they are asking about the concept of p-value, rather than its actual value in this problem?

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