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

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