Solution Found!
Simulation Simulate drawing 100 simple random samples of
Chapter 6, Problem 36AYU(choose chapter or problem)
Simulation Simulate drawing 100 simple random samples of size n = 15 from a population that is normally distributed with mean 100 and standard deviation 15 .
(a) Test the null hypothesis \(H_0:\mu=100\) versus \(H_1:\mu \ne 100\) for each of the 100 simple random samples.
(b) If we test this hypothesis at the \(\alpha=0.05\) level of significance, how many of the 100 samples would you expect to result in a Type I error?
(c) Count the number of samples that lead to a rejection of the null hypothesis. Is it close to the expected value determined in part (b)?
(d) Describe how we know that a rejection of the null hypothesis results in making a Type I error in this situation.
Questions & Answers
QUESTION:
Simulation Simulate drawing 100 simple random samples of size n = 15 from a population that is normally distributed with mean 100 and standard deviation 15 .
(a) Test the null hypothesis \(H_0:\mu=100\) versus \(H_1:\mu \ne 100\) for each of the 100 simple random samples.
(b) If we test this hypothesis at the \(\alpha=0.05\) level of significance, how many of the 100 samples would you expect to result in a Type I error?
(c) Count the number of samples that lead to a rejection of the null hypothesis. Is it close to the expected value determined in part (b)?
(d) Describe how we know that a rejection of the null hypothesis results in making a Type I error in this situation.
ANSWER:Step 1 of 5
We have to generate 100 simple random samples of normal distribution with mean 100 and std dev 15
From excel
> select data - random number generation
> normal - enter the size, mean and std dev
> ok
Some of the samples are
151.8368 |
89.61051 |
114.9899 |
105.4591 |
88.12779 |
113.9714 |
121.95 |
108.0325 |
115.7702 |
75.54064 |
112.0821 |
90.30686 |
133.3383 |
93.30242 |
104.4663 |
110.4245 |
133.1775 |
114.7628 |
117.9119 |
101.8654 |
105.9029 |
88.69077 |
112.8239 |
115.4176 |
91.17598 |
104.3944 |
75.96437 |
86.68292 |
101.1308 |
99.96615 |
117.0257 |
97.42452 |
102.4242 |
100.9111 |
107.4128 |
87.79685 |
88.10422 |
91.1637 |
77.54205 |
120.7646 |
109.2117 |
106.0495 |
-43.0511 |
72.2138 |
101.2044 |
84.31333 |
109.713 |
111.1876 |
84.22783 |
78.34695 |
122.0713 |
98.84853 |
128.6121 |
91.55248 |
97.02998 |
100.733 |
85.16059 |
123.5748 |
97.81264 |
72.66073 |
120.452 |
122.5534 |
101.148 |
84.42786 |
97.04517 |
105.3538 |
82.38654 |
87.19591 |
111.7393 |
87.30457 |
76.6437 |
110.388 |
122.7544 |
106.2429 |
90.05092 |
96.42828 |
123.6899 |
100.3047 |
93.00956 |
90.73697 |
84.18987 |
103.1141 |
116.9886 |
92.03758 |
122.9745 |
111.2164 |
99.22569 |
92.9263 |
104.7997 |
104.726 |
Mean = 100.6019 and std dev = 15.43