1) the heat evolved in calories per gram of a cement mixture is approximately no
ID: 3127671 • Letter: 1
Question
1) the heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100 and the standard deviation is 2. We wish to test Ho: u= 100 vs H1 (does not equal) 100 with a sample of n=9 specimens.a) find the type I error probability alpha b) find the probably of type II error beta when the true mean hear evolved is 103. Find the power of the test c) find the probably of type II error beta when the true mean heat evolved is 105. Find the power of the test. d) compare the power of the test between b and c and explain the difference
Explanation / Answer
a. Probability of Type I error is the significance level of the test that is alpha=0.05.
b. At n=9, and alpha=0.05, the z critical value is 1.645. The test is two-tailed test, and this z value correspond to that particular(unknown) value, for which one fail sto reject a false null hypothesis (p=0.95).
Therefore, 1.645=(Unknown-mu)/sigma
1.645=(x-100)/2
x=103.29
Therefore, probability of Type II error is as follows:
z=(103.29-103)/2=0.145 [Answer]
c. z=(103.29-105)/2=-0.855
The probability is 1-0.855=0.145.
d. For the first case, the probability was calculated as follows:
P(Z<(103.29-103)/2) and in the second case P(Z>(103.229-105)/2)
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