A new quality assurance process developed in Seoul by Mr Yu for a newly introduced Cement results in a mean strength of 5000 with a standard deviation of 120 kilograms. In order for Mr Yu to test the null hypothesis that ? = 5000 against the alternative that ? < 5000, He random sampled 50 fragments of this cement and tested them. If his critical region was defined to be ? < 4970. What will be his probability of not committing type II error when ? = 4960.
A new quality assurance process developed in Seoul by Mr Yu for a newly
introduced Cement results in a mean strength of 5000 with a standard
deviation of 120 kilograms. In order for Mr Yu to test the null hypothesis that
? = 5000 against the alternative that ? < 5000, He random sampled 50 fragments
of this cement and tested them. If his critical region was defined to be ? < 4970. What
will be his
There are two types of errors namely, type l error and type ll error.
Type l error : Type l error occurs when the null hypothesis is rejected when it is true. Probability of type l error is α.
Type ll error : This error occurs when the null hypothesis is accepted when it is false. Probability of type ll error is β.
We have to calculate the probability of not committing type ll error (that is, 1–β) when,
µ = 4960.
According to the question,
Sample size (n) = 50, and
Standard deviation (σ) = 120
Critical region : x̄ < 4970
(Critical region is defined as the set of values of the test statistic of a statistical test for which the null hypothesis is rejected).
Probability of type ll error (β) is calculated using,
β = P( do not reject H0 | µ = 4960)
Where, H0 = Null hypothesis.
(x̄ ≥ 4970 is a region of not rejecting null hypothesis)
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