Reading 11: Hypothesis Testing - LOS c, (Part 1) ～ Q1-5 class, percent, critical, freedom

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1.For a t-distributed test statistic with 30 degrees of freedom, a one-tailed test specifying the parameter greater than some value and a 95 percent confidence level, the critical value is:

A)   1.697.

B)   1.640.

C)   2.042.

D)   1.310.

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

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

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

3.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 I error over a type II error.

B)   two tailed test over a one tailed test.

C)   higher level of significance.

D)   type II error over a type I error.

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

A)   avoiding type II errors.

B)   avoiding type I errors.

C)   avoiding type III errors.

D)   the null hypothesis.

5.The power of the test is:

A)   the probability of rejecting a true null hypothesis.

B)   equal to the level of significance.

C)   the probability of rejecting a false null hypothesis.

D)   equal to the level of confidence.

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答案和详解如下：

1.For a t-distributed test statistic with 30 degrees of freedom, a one-tailed test specifying the parameter greater than some value and a 95 percent confidence level, the critical value is:

A)   1.697.

B)   1.640.

C)   2.042.

D)   1.310.

The correct answer was A)

This is the critical value for a one-tailed probability of 5% and 30 degrees of freedom.

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

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

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

The correct answer was A)

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

3.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 I error over a type II error.

B)   two tailed test over a one tailed test.

C)   higher level of significance.

D)   type II error over a type I error.

The correct answer was D)

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).

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

A)   avoiding type II errors.

B)   avoiding type I errors.

C)   avoiding type III errors.

D)   the null hypothesis.

The correct answer was B)

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.

5.The power of the test is:

A)   the probability of rejecting a true null hypothesis.

B)   equal to the level of significance.

C)   the probability of rejecting a false null hypothesis.

D)   equal to the level of confidence.

The correct answer was C)

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).