Hypothesis Testing
A hypothesis test is to be conducted using an alpha = .05 level. This means:
there is a maximum 5 percent chance that a true null hypothesis will be rejected.
The critical value in a null hypothesis test is called alpha. True / False
False
The significance level in a hypothesis test corresponds to the maximum probability that a Type I error will be committed. True False
True
The power of a test is measured by its capability of:
rejecting a null hypothesis that is false.
When using the p-value method, the null hypothesis is rejected when the calculated p-value > α. True / False
False (p-value is not less than, do not reject)
If the probability of a Type I error is set at 0.05, then the probability of a Type II error will be 0.95. True False
False
If the sample data lead the decision maker to reject the null hypothesis, the alpha level is the maximum probability of committing a Type II error. True False
False
In a one-tailed hypothesis test, the larger the significance level, the greater the critical value will be. True False
False
The impact on the margin of error for a confidence interval for an increase in confidence level and a decrease in sample size is unknown since these changes are contradictory. True / False
False
Choosing an alpha of 0.01 will cause beta to equal 0.99. True/False?
False (alpha + beta does not = 1)
When using the t-distribution in a hypothesis test, the population does not need to be assumed normally distributed. True False
False (it is assumed to be normally distributed)
A report recently submitted to the managing partner for a market research company stated "the hypothesis test may have resulted in either a Type I or a Type II error. We won't know which one occurred until later." This statement is one that we might correctly make for any hypothesis that we have conducted. True False
False
A two-tailed hypothesis test is used when the null hypothesis looks like the following: H0 : (x-bar) = 100. True False
False
All other factors held constant, the higher the confidence level, the closer the point estimate for the population mean will be to the true population mean. True False
False
Generally, it is possible to appropriately test a null and alternative hypotheses using the test statistic approach and reach a different conclusion than would be reached if the p-value approach were used. True False
False
Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures and share little in common with each other. True/False
False
If a hypothesis test leads to incorrectly rejecting the null hypothesis, a Type II statistical error has been made. True / False
False
For testing a research hypothesis, the burden of proof that a new product is no better than the original is placed on the new product, and the research hypothesis is formulated as the null hypothesis. True/False
False (research hypothesis is the alternative)
In a two-tailed hypothesis test the area in each tail of the rejection region is equal to α.
False (should be: α/2)
In a hypothesis test, the p-value measures the probability that the alternative hypothesis is true. True False
False- always measures the null hypothesis
A report recently published in a major business periodical stated that the average salary for female managers is less than $50,000. If we were interested in testing this, the following null and alternative hypotheses would be established: H0 : μ ≥ 50,000 Hα : μ 50,000 True False
True
A two-tailed hypothesis test with α = 0.05 is similar to a 95 percent confidence interval. True /False
True
In conducting a hypothesis test where the conclusion is to reject the null hypothesis, then either a correct decision has been made or else a Type I error. True False
True
In hypothesis testing, the null hypothesis should contain the equality sign.
True
In testing a hypothesis, statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data. True False
True
Of the two types of statistical errors, the one that decision makers have most control over is Type I error. True False
True
The director of the city Park and Recreation Department claims that the mean distance people travel to the city's greenbelt is more than 5.0 miles. Assume that the population standard deviation is known to be 1.2 miles and the significance level to be used to test the hypothesis is 0.05 when a sample size of n = 64 people are surveyed. Given this information, if the sample mean is 15.90 miles, the null hypothesis should be rejected. True False
True
To calculate beta requires making a "what if" assumption about the true population parameter, where the "what-if" value is one that would cause the null hypothesis to be false.
True
When deciding the null and alternative hypotheses, the rule of thumb is that if the claim contains the equality (e.g., at least, at most, no different from, etc.), the claim becomes the null hypothesis. If the claim does not contain the equality (e.g., less than, more than, different from), the claim is the alternative hypothesis. True False
True
When someone has been accused of a crime the null hypothesis is: H0 : innocent. In this case, a Type I error would be convicting an innocent person. True / False
True
When using the p-value method for a two-tailed hypothesis, the p-value is found by finding the area in the tail beyond the test statistic, then doubling it. True/False
True
A contract calls for the mean diameter of a cylinder to be 1.50 inches. As a quality check, each day a random sample of n = 36 cylinders is selected and the diameters are measured. Assuming that the population standard deviation is thought to be 0.10 inch and that the test will be conducted using an alpha equal to 0.025, what would the probability of a Type II error be?
a. Approximately 0.1267 **b. Can't be determined without knowing the "true" population mean.** c. 0.975 d. About 0.6789
If the p value is less than α in a two-tailed test then:
the null hypothesis should be rejected.
