Why it is generally impossible to calculate exactly the power of an experiment.
If the the probability of committing a type-2 error is 7%. What is the power of the experiment?
What are two ways you can increase the power of an experiment.
1. Power of a test is the probability of rejecting the null hypothesis correctly, ie rejecting it when it is false. Since power = 1- probability of making type II error, we generally get the best approximate value and not the exact value.
2. Power = 1- probability of making type II error= 1-0.07= 0.93 ie 93%
3. Two ways to increase power:
a) Increases sample size n of the test (so that random error is reduced)
b) Increase the significance level alpha
Why it is generally impossible to calculate exactly the power of an experiment. If the the...
State whether the following statements true or false, and Why? 1. The type I error and type II error are related. A decrease in the probability of one generally results in an increase in the probability of the other. 2. The size of the critical region, and therefore the probability of committing a type I error, can always be reduced by adjusting the critical value(s). 3. An increase in the sample size n will reduce α and β simultaneously. 4....
5. A bowl contains ten marbles of which 0 are white while the others are black. In order to test the null hypothesis H0 : θ-1 against H1: θ > 1, five of the marbles are randomly drawn with replacement and the null hypothesis is rejected if at least two of the five drawn are white. (a) What is the probability of committing a Type I error? (21 (b) What is the probability of committing a Type II error when...
Holding everything else is fixed, which will decrease when the probability of committing a Type I error is reduced? Two answers are correct: 1. level of significance 2. β 3. power 4. level of confidence 5. probability of committing a type II error 6. confidence coefficient
1. Which of the following statements are not generally true? a. A type I error is usually more serious than a type II error. b. A type II error is usually more serious than a type I error. c. A test with significance level is one for which the type I error probability is controlled at the specified level. d. When an experiment and a sample size are fixed, then decreasing the size of the rejection region to obtain...
23. Calculate the probability of getting exactly two sixes and one five when rolling five dice. Do this in two different ways, as follows. (a) First calculate the probability that two of the five dice land sixes, and then multiply this by the probability that one of the remaining three lands a five. (note: The remaining three dice have only five ways in which they can land.) (b) Next calculate the probability that one of the five dice lands a...
Determine if the following probability experiment represents a binomial experiment. If not, explain why. If the probability experiment is a binomial experiment, state the number of trials, and probability of success, p. An investor randomly purchases 18 stocks listed on a stock exchange. Historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 44%. The number of stocks that increase in value is recorded Select the correct choice below and...
QUESTION 5
The power of the statistical test is zero (0) when the mean is
52, the sample size is 25, and the standard deviation is 2, and the
probability of committing Type II error when P is one (1) (previous
problem).
True
False
5 5
A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He believes that the mean systolic blood pressure, H. of CEOs of major corporations is less than 132 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test and measures the systolic blood pressures of a random sample of 50 CEOs of major corporations. Suppose that the population of systolic blood...
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The average retirement age for a certain country was reported to be 56.4 years according to an international group dedicated to promoting trade and economic growth. With the pension system operating with a deficit, a bill was introduced by the government during the summer to raise the minimum retirement age from 60 to 62 Suppose a survey of 49 retiring citizens is taken to investigate whether the new bil has raised the average age at which people actually retire. Assume...