chunty

The power of the test is:

A) the probability of rejecting a false null hypothesis.

B) the probability of rejecting a true null hypothesis.

C) equal to the level of confidence.

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This is the definition of the power of the test: the probability of correctly rejecting the null hypothesis (rejecting the null hypothesis when it is false).

chunty

A bottler of iced tea wishes to ensure that an average of 16 ounces of tea is in each bottle. In order to analyze the accuracy of the bottling process, a random sample of 150 bottles is taken.  Using a t-distributed test statistic of -1.09 and a 5% level of significance, the bottler should:

A) not reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

B) not reject the null hypothesis and conclude that bottles do not contain an average of 16 ounces of tea.

C) reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

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Ho: µ = 16; Ha: µ ≠ 16. Do not reject the null since |t| = 1.09 < 1.96 (critical value).

chunty

If the null hypothesis is innocence, then the statement “It is better that the guilty go free, than the innocent are punished” is an example of preferring a:

A) type II error over a type I error.

B) higher level of significance.

C) type I error over a type II error.

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The statement shows a preference for accepting the null hypothesis when it is false (a type II error), over rejecting it when it is true (a type I error).

chunty

A goal of an “innocent until proven guilty” justice system is to place a higher priority on:

A) avoiding type II errors.

B) the null hypothesis.

C) avoiding type I errors.

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In an “innocent until proven guilty” justice system, the null hypothesis is that the accused is innocent. The hypothesis can only be rejected by evidence proving guilt beyond a reasonable doubt, favoring the avoidance of type I errors.

chunty

An analyst calculates that the mean of a sample of 200 observations is 5. The analyst wants to determine whether the calculated mean, which has a standard error of the sample statistic of 1, is significantly different from 7 at the 5% level of significance. Which of the following statements is least accurate?:

A) The mean observation is significantly different from 7, because the calculated Z-statistic is less than the critical Z-statistic.

B) The alternative hypothesis would be Ha: mean > 7.

C) The null hypothesis would be: H0: mean = 7.

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The way the question is worded, this is a two tailed test.The alternative hypothesis is not Ha: M > 7 because in a two-tailed test the alternative is =, while < and > indicate one-tailed tests. A test statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean – hypothesized mean) / (standard error of the sample statistic) = (5 - 7) / (1) = -2. The calculated Z is -2, while the critical value is -1.96. The calculated test statistic of -2 falls to the left of the critical Z-statistic of -1.96, and is in the rejection region. Thus, the null hypothesis is rejected and the conclusion is that the sample mean of 5 is significantly different than 7. What the negative sign shows is that the mean is less than 7; a positive sign would indicate that the mean is more than 7. The way the null hypothesis is written, it makes no difference whether the mean is more or less than 7, just that it is not 7.

chunty

Given a mean of 10% and a standard deviation of 14%, what is a 95% confidence interval for the return next year?

A) -4.00% to 24.00%.

B) -17.00% to 38.00%.

C) -17.44% to 37.44%.

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10% +/- 14(1.96) = -17.44% to 37.44%.

chunty

A researcher is testing whether the average age of employees in a large firm is statistically different from 35 years (either above or below). A sample is drawn of 250 employees and the researcher determines that the appropriate critical value for the test statistic is 1.96. The value of the computed test statistic is 4.35. Given this information, which of the following statements is least accurate? The test:

A) indicates that the researcher will reject the null hypothesis.

B) indicates that the researcher is 95% confident that the average employee age is different than 35 years.

C) has a significance level of 95%.

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This test has a significance level of 5%. The relationship between confidence and significance is: significance level = 1 − confidence level. We know that the significance level is 5% because the sample size is large and the critical value of the test statistic is 1.96 (2.5% of probability is in both the upper and lower tails).

chunty

Which of the following statements about hypothesis testing is most accurate?

A) A Type I error is rejecting the null hypothesis when it is true, and a Type II error is accepting the alternative hypothesis when it is false.

B) When the critical Z-statistic is greater than the sample Z-statistic in a two-tailed test, reject the null hypothesis and accept the alternative hypothesis.

C) A hypothesized mean of 3, a sample mean of 6, and a standard error of the sampling means of 2 give a sample Z-statistic of 1.5.

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Z = (6 - 3)/2 = 1.5. A Type II error is wrongly accepting the null hypothesis. The null hypothesis should be rejected when the sample Z-statistic is greater than the critical Z-statistic.

chunty

If the probability of a Type I error decreases, then the probability of:

A) incorrectly accepting the null decreases.

B) incorrectly rejecting the null increases.

C) a Type II error increases.

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If P(Type I error) decreases, then P(Type II error) increases. A null hypothesis is never accepted. We can only fail to reject the null.

chunty

Which of the following statements about hypothesis testing is most accurate? A Type II error is the probability of:

A) rejecting a true alternative hypothesis.

B) failing to reject a false null hypothesis.

C) rejecting a true null hypothesis.

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The Type II error is the error of failing to reject a null hypothesis that is not true.