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  1. Review all student work for calculating a confidence interval for a sample mean. Redo their work and confirm that it is correct, or correct it and note the errors. What is the final margin of error E? What is the final confidence interval? Offer an example sample mean that would fit into the confidence interval. Offer an example sample mean that would be outside of the confidence interval.
  2. Review all student work for calculating a confidence interval for a sample proportion. Redo their work and confirm that it is correct, or correct it and note the errors. What is the final margin of error E? What is the final confidence interval? Offer an example sample proportion that would fit into the confidence interval. Offer an example sample proportion that would be outside of the confidence interval.

Student 1 post Stephanie


For this week I chose the dataset (exam scores), used the population of 30 (n = 30). Calculations for the mean confidence interval were straight-forward, to calculate a confidence interval proportion, I looked at exam scores above 90%. I started by sorting my data from the largest to smallest (note the student numbers are no longer sequential). For this small dataset, it was a simple matter to count 8 scores above 90%, and go from there. Finally, I rounded all calculations to 2 decimal places, because I found this easier.

95% CI for mean: 76.59 < mu < 85.15

95% CI score > 90%: 0.11 < P(>90%) < 0.42

Excel formulas used:

Sample Mean (x bar): = average (data array)

Sample std dev: = stdev.s (data array) Note the “.s” at the end. Excel knows the difference between sample and population when calculating std dev.

Error (mean): = 1.96* (sample std dev)/sqrt(n)

Lower and Upper CI limits = Sample mean – Error, and + Error

Note the CI is around the population parameter (mu, not xbar). We know what xbar is for our sample. We are making an inference about the population. In plain language, there is a 95% probability that this interval contains the true population average. That means, there is a 5% probability that the TRUE value lies outside our interval. Why would that happen? One possible (common explanation) – sampling error. There may have been something skewed in our survey methodology.

Phat (proportion estimate) = # of observations/n

Error (proportion): = 1.96*(sqrt(phat*(1-phat)/n)) Count the number of left and right parenthesis. They must be the same for the formula to work correctly. In this case, 3 lefts, 3 rights. Good to go.

Confidence interval same as for mean. Sample estimate +/- error.

Student # Exam Score

4          100.00

30        100.00 Sample size n              30

24        99.00 Sample mean                 80.87

5          96.00 Sample std dev             11.96

14        95.00

15        93.00 Error (mean)                  4.28

29        93.00

6          92.00 LCI (mean)                    76.59

2          89.00 UCI (mean)                   85.15

7          85.00

9          84.00 Probability of score > 90%

13        84.00

25        84.00 Observations                 8

22        82.00 Phat                               0.27

23        82.00

17        81.00 Error (proportion)         0.16

18        80.00

1          77.00 LCI (proportion)           0.11

11        77.00 UCI (proportion)           0.42

28        77.00

20        76.00

16        73.00

3          71.00

12        71.00

21        71.00

19        69.00

27        65.00

10        62.00

8          59.00

26        59.00


Student 2 post Jennie

 

  1. My sample is: 31,34,54,32,34,37,47,37,47,54,34,54,38,32,31,30,43,54,23,21,32,34,36,54,32,37,32,34,35,34
  2. My sample mean is: 38
  3. My sample standard deviation: 9
  4. E=1.96(9)= 17.64
    Sqrt(30)= 5.477
    17.64/5.477

    E=3.22
    Confidence Interval= 34.78 and 41.22

     

1.  My sample is:

7,5,3,4,6,8,5,3,2,4,5,6,7,4,2,3,7,8,9,7,6,5,4,3,6,7,8,9,7,6,

2.  My mean is: 6

3.  E=1.96* sqrt(6*(1-6)/30)= -.80

           E= -.80

          Confidence Interval= 5.2 and 6.8



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