Practice Questions for Midterm
Define and explain the following terms. For each term, describe how it is used in the process of statistical testing.
- significance level
- type II error
- null hypothesis
- one-tail test
- confidence level
State the effect on the width of a confidence interval of
- a larger sample size
- a higher confidence level
- a larger sample standard deviation
Someone claims that auto mechanics earn more than plumbers. A sample of 12 auto mechanics finds that they earn $34,000 a year with a standard deviation of $3,000. A sample of 14 plumbers finds that they earn $32,000 a year with a standard deviation of $4,000. Is the difference statistically significant at the 5 percent level?
In large corporations, 90 percent of personal computers use Windows, with only 10 percent Macs. In a sample of 250 high school computers, 212 use Windows and 38 are Macs. Is the difference between the proportion of Windows computers in schools and in corporations statistically significant at the 1 percent level?
- A trainer wants to test whether a particular bridle helps horses race faster. Can this be tested using one sample? Using two samples? Using matched pairs? Explain.
- What needs to be specified in order to be able to calculate the power of a test?
- When a test result is not statistically significant, why do we say that "we fail to reject the null hypothesis" rather than "we accept the null hypothesis"?
- When we say that a 90 percent confidence interval for m is 146.5 plus or minus 2.2, are we saying that there is a 90 percent probability that m is between 144.3 and 148.7? Give a more carefully worded statement of the meaning of this confidence interval.