Analysis 1 Organization X created a scheme of rating...

Analysis 1 Organization X created a scheme of rating employees on a 1-100 scale. The scale is normed to 85 as acceptable performance (i.e., the population mean of performance using this scale is 85). The variance, on the other hand, is unknown. You are tasked as the chief researcher of this organizational project to run the appropriate test to determine if there is a difference between this department (n = 57) and the normative performance score. Run the test as a two-tailed test at $\alpha = .05$. Null Hypothesis ($H_0$) Alternative Hypothesis ($H_1$) df $t_{critical}$ $\mu$ M $S^2$ $S_M$ t Reject? Conclusions

Transcript

0:00 All right.

00:01 So we have some data here that comes from a journal, and they're studying the relationship between voluntary organization turnover.

00:12 And so we have data on people who were stares.

00:16 Performance ratings for people who were stairs are a sample of 175 people who stayed.

00:21 And this is their performance rating, and this is this known standard deviation of the stairs.

00:29 And the levers, the voluntary leaving of the company, there are a sample of 140 of them, their mean was 14 .7, standard deviation sigma for that group is 4 .5.

00:42 And we are going to test the hypothesis that they mean score, the mean performance rating of the lever group, i'm calling group two, is greater than that of these stairs.

00:58 So we're going to calculate the difference is x bar 1 minus x bar 2.

01:02 That's the means.

01:03 We take the difference as negative 1 .9 and we're told to do it is 1 minus 2, so it's negative 1 .9.

01:11 And the first thing we're do is make a 99 % confidence interval about it, about the difference.

01:20 So this is going to be x bar 1 minus x bar 2 plus minus z alpha over 2.

01:30 But the alpha is going to be 0 .01, cut that in half.

01:38 And then we multiply it by the standard error.

01:41 And the standard error for a difference of means given the population standard deviations, which we are.

01:48 It's going to be sigma squared 1 over the sample size plus sigma squared of the second group divided by its sample size.

01:58 And this is called the standard error.

02:00 And we're going to use that.

02:03 And then the standard error.

02:05 Standard error times the z.

02:07 This is called the margin of error.

02:09 And when i'm making a confidence interval, i like to call it out.

02:12 So now it's a matter of plugging in our values for our formulas.

02:17 So here's the standard error when you calculate it out.

02:19 Just make sure you take the square of the standard evations.

02:23 Just square those to get the variances.

02:26 And that's what the sigma squared is.

02:28 And this is standard error.

02:30 .472.

02:31 Don't round until the very end.

02:32 So i'm using the full precision my spreadsheet gave me.

02:35 But even if you just put in the values into a formula, and then wait till we get everything out, then we're good to go.

02:40 The margin of error is this, 1 .216.

02:44 So we add that to and subtract it from the difference.

02:47 And we get this is our interval, negative 3 .12 up to negative 0 .68.

02:56 So this is the 99 % confidence interval for the difference in the performance rating for stairs and levers.

03:03 And since 0 is not contained in it, 0 is outside the interval.

03:07 If you think about a number line, the negatives are down here.

03:12 Here's zero and positives are up here...

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