Question

In: Statistics and Probability

Question3: Consider the following 14 independent measurements from a normal distribution: Independent measurements 20 18 11...

Question3: Consider the following 14 independent measurements from a normal distribution:

Independent measurements
20 18 11 20 16 14 15 15 14 13 11 18 20 9
1) What is the standard error of the sample mean?
0.9936
3.5826
0.9575
3.4303

2) Calculate a 99% confidence interval for the population mean.
[5.8831,24.6883]
[12.9734,17.5980]
[12.4015,18.1700]
[12.7480,17.8234]

Solutions

Expert Solution

20 4.7142857 22.22448980
18 2.7142857 7.36734694
11 -4.2857143 18.36734694
20 4.7142857 22.22448980
16 0.7142857 0.51020408
14 -1.2857143 1.65306122
15 -0.2857143 0.08163265
15 -0.2857143 0.08163265
14 1.2857143 1.65306122
13 -2.2857143 5.22448980
11 -4.2857143 18.36734694
18 2.7142857 7.36734694
20 4.7142857 22.22448980
9 -6.2857143 39.51020408

  


a) The standard error of the sample mean

  

Answer: 0.9575

b) We need to construct the 99% confidence interval for the population mean μ.

The critical value for α=0.01 and df = n-1 =14-1= 13, tc​= t1−α/2;n−1​=3.012.

The corresponding confidence interval is computed as shown below:

  

  

Answer: (12.4015, 18.1700)


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