If you multiply six positive numbers, the product’s sign will be . If you multiply six negative numbers, the product’s sign will
2 answers:
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Answer:
A.the type 1 error probability is
B. β = 0.0122
C. β = 0.0000
Step-by-step explanation:
Given that:
Mean = 100
standard deviation = 2
sample size = 9
The null and the alternative hypothesis can be computed as follows:
A. If the acceptance region is defined as , find the type I error probability
.
Assuming the critical region lies within or
, for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is
∴
when
From the standard normal distribution tables
Thus, the type 1 error probability is
B. Find beta for the case where the true mean heat evolved is 103.
The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis
Thus;
β = P( type II error) - P( fail to reject )
∴
Given that
From standard normal distribution table
β = 0.0122 - 0.0000
β = 0.0122
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?
Given that
From standard normal distribution table
β = 0.0000 - 0.0000
β = 0.0000
The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.