Question

Test of Hypotheses and Test for Single Mean

1) How are Type 1 and Type II errors committed in the following test? For each error type, explain the resulting conclusion and the error in it.
Ho: The accused is innocent. vs. Ha: The accused is guilty.
2) Solve the following problems by a test for single mean and a (1-α)100% confidence interval 8 of significance, can we reject the claim that on the average such orders are filled in more than 10 days?
b) Five measurements of the tar content of a certain kind of cigarette yielded 14.5, 14.2, 14.4, 14.8, and 14.1 mg/cig. Is the difference between the mean of this sample and μ=14.1 (as claimed on the packages) significant at α=0.05.

A random sample from a company’s very extensive files shows that orders for a certain piece of machinery were filled in 12, 10, 17, 14, 13, 18, 11, and 9 days. At the α=0.05 level of significance, can we reject the claim that on the average such orders are filled in more than 10 days?

Answer 1

1)

type i error - when we reject the null hypothesis even when null hypothesis is true

type ii error- when we fail to reject the null hypothesis, even when null hypothesis is false

hence type i error would be to conclude that accused is guilty even though accused in innocent

whereas type ii error would be to fail to conclude that accused is guilty when in fact accused is guilty