Statistics - EXAM #4 Review
A significance level that is often used in hypothesis testing by researchers and statisticians is: A. 0.05 B. 0.50 C. 0.25 D. 0.15
A. 0.05
*Shaded areas on graph on either side (middle not shaded) The shaded area could be a p-value for a test with a _____________ alternative hypothesis since both tails are of equal size.
two-tailed
*shaded area is middle of graph. not shaded on either sides The shaded area could not be a p-value because ___________________________________.
it does not include tail areas
In hypothesis testing, the null hypothesis is best described by which of the following statements? A. The null hypothesis always gets the benefit of the doubt and is assumed to be true throughout the hypothesis testing procedure. B. The null hypothesis is always assumed to be false throughout the hypothesis testing procedure. C. The null hypothesis can be chosen by a computer. D. Both A and C are correct
A. The null hypothesis always gets the benefit of the doubt and is assumed to be true throughout the hypothesis testing procedure. explanation: the null hypothesis is assumed to be true unless observation strongly indicates otherwise
A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05. He randomly selects 300 light bulbs and finds 27 that are defective. Symbolically, the null and alternative hypothesis are as follows: Ho: p = 0.07 Ha: p > 0.07. The janitor calculates a p-value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the p-value. A. The p-value tells us that if the defect rate is 0.07, then the probability that the janitor will have 27 or more defective light bulbs out of 300 is approximately 0.087. At a significance level of 0.05, this would not be an unusual outcome. B. The p-value tells us that the probability of concluding that the defect rate is equal to 0.07, when in fact it is greater than 0.07, is approximately 0.087. C. The p-value tells us that the true population rate of defective light bulbs is approximately 0.087. D. None of these
A. The p-value tells us that if the defect rate is 0.07, then the probability that the janitor will have 27 or more defective light bulbs out of 300 is approximately 0.087. At a significance level of 0.05, this would not be an unusual outcome.
In hypothesis testing, when should the null hypothesis be rejected? A. When the p-value is less than the significance level B. When the p-value is less than the value in the null hypothesis C. When the p-value is greater than the significance level D. When the p-value is greater than the value in the null hypothesis
A. When the p-value is less than the significance level
The value in the null hypothesis comes from what? A. The sample statistic B. Assuming the status quo about the population C. The significance level of the hypothesis test D. The confidence level of the confidence interval
B. Assuming the status quo about the population
Which of the following phrases should not be used when writing a conclusion to a hypothesis test? A. Fail to reject the null hypothesis. B. The null hypothesis cannot be rejected. C. The null hypothesis is accepted as true. D. All of the above are correct ways of writing a hypothesis test conclusion.
C. The null hypothesis is accepted as true. explanation: if the power of the test is low, the null hypothesis may be false and yet the evidence may be insufficient for rejecting it
Which of the following does not describe the null hypothesis? A. is a conservative statement about the population parameter B. It is a status-quo, business-as-usual statement about the population parameter C. It is the research hypothesis D. All of the above statements describe the null hypothesis
C. It is the research hypothesis explanation: the alternative hypothesis is the research hypothesis
In hypothesis testing, what does a negative test statistic mean? A. The assumed population proportion in the null hypothesis was less than the sample proportion B. The test was done incorrectly C. The sample proportion was less than the assumed population proportion in the null hypothesis D. The sampling distribution conditions were not met
C. The sample proportion was less than the assumed population proportion in the null hypothesis explanation: the test statistic is caluclated by subtracting the assumed population proportion in the null hypothesis from the sample proportion, then dividing by a positive number. If the sample proportion is less than the assumed population, the test statistic will be negative
What is the significance level of a test? A. The same as the population proportion B. The probability that the null hypothesis is true C. The probability of rejecting the null hypothesis when, in fact, the null hypothesis is false D. The probability of rejecting the null hypothesis when, in fact, the null hypothesis is true
D. The probability of rejecting the null hypothesis when, in fact, the null hypothesis is true explanation: it is the likelihood of obtaining a sample statistic distinct from the predicted population parameter to the extent that it makes the predicted population parameter seem incorrect when, in fact, it is correct
T/F: Sample evidence can prove that a null hypothesis is true.
FALSE explanation: although sample data is used to test the null hypothesis, it cannot be stated with 100% certainty that the null hypothesis is true. It can only be determined whether the sample data supports or does not support the null hypothesis.
The null hypothesis is always a statement about a: a. population parameter b. sample statistic
a. population parameter
Which of the following best describes hypotheses? a. statements about population parameters b. statements that cannot be tested c. statements that are always true d. statements about sample statistics
a. statements about population parameters
In hypothesis testing, what does an extreme value for the test statistic indicate? a. The test was done incorrectly b. The sample was not random c. The null hypothesis is not true d. The null hypothesis is true
c. The null hypothesis is not true explanation: a test statistic of zero means that the value of the sample statistic is exactly the same as the hypothesized value of the population parameter, so an extreme value for the test statistic contradicts the null hypothesis
A researcher carried out a hypothesis test using a two-tailed alternative hypothesis. Which of the following z-scores is associated with the smallest p-value? Explain. a. z = -0.44 b. z = -0.93 c. z = -2.18 d. z = -3.37 Explain. A. The z-score closest to 0 has the smallest tail area and thus has the smallest p-value. B. The z-score closest to 0 has the largest tail area and thus has the smallest p-value. C. The z-score farthest from 1 has the largest tail area and thus has the smallest p-value. D. The z-score farthest from 0 has the smallest tail area and thus has the smallest p-value.
d. z = -3.37 D. The z-score farthest from 0 has the smallest tail area and thus has the smallest p-value.
