Chapter 8 Q17

Chapter 8 Q17

Use descriptive stats to get the data below:
Rating

Mean 6.34
Standard Error 0.30587446
Median 6.5
Mode 8
Standard Deviation 2.16285903
Sample Variance 4.67795918
Kurtosis -1.18062982
Skewness -0.14449225
Range 8
Minimum 2
Maximum 10
Sum 317
Count 50
Confidence Level(95.0%) 0.61467772

Now, the question asks us for a 95% confidence interval. n>30 so we can use the CLT. Note that the margin of error given above is for the t distribution. The margin of error for the normal distribution (that is using the CLT) will be a little narrower.
We can calculate this by hand or using Excel. Let’s have fun (!) and do both:
The M of E by hand for 95% is 1.96*0.306 (rounding up) = 0.6
In Excel we go =confidence(=0.05,2.162,50) = 0.6
So the Confidence Interval is the mean plus or minus the Margin of Error:
6.34 – 0.6 to 6.34 + 0.6 or 5.74 to 6.94
Notice that the Margin of Error for the t dist is indeed slightly larger than that for the normal distribution