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1. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant.
a. Increasing the alpha level from .01 to .05.
b. Changing from a one-tailed test to a two-tailed test.
2. A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of 80 and a standard deviation of 20. The researcher expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with alpha = .05.
a. Compute the power of the test if the researcher uses a sample of n = 16 individuals.
b. Compute the power of the test if the researcher uses a sample of n = 25 individuals.
A research study reports t(14) = 2.17. How many individuals participated in the study? Is this t statistic sufficient to reject the null hypothesis using a two-tailed test with alpha = 0.05?
An urn contains 8 green balls, 5 red balls, and 7 white balls. How many ways are there to draw a green ball or a red ball?
From historical data, Harry's Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes.
A random sample of 77 eighth grade students' scores on a nation mathematics assessment test has a mean score of 278 with a standard deviation of 31.
Which approach is most preferred and why? Optimistic, conservative, or minimax regret. Also, is establishing the most appropriate approach before analysising the problem important for the decision maker?
What is the expected number of customers that will have to wait more than 6 hours?
A fastener manufacturing company uses a chi-square goodness of fit test to determine if a population of all lengths of ¼ inch bolts it manufactures is distributed according to a normal distribution.
What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
What proportion of observed variation in hardness can be explained by the simple linear regression model relationship between hardness and elapsed time? (Give the answer to three decimal places.)
In relative frequency histogram for a large set of GPAs, the mean and the standard deviation are 2.10 and 0.21 respectively. What proportion of GPAs falls within 1.68 and 2.52?
If you randomly assign participants to groups, can you suppose the groups are equivalent at the beginning of the study?
A random sample of 50 households revealed a mean of $112,000 and a standard deviation of $40,000. What is the standard error of the mean?
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