Question

True?For the methods of this section, which of the following statements are true?

a.When testing a claim with ten matched pairs of heights, hypothesis tests using the P-valuemethod, critical value method, and confidence interval method will all result in the same conclusion.

b.The methods of this section are robustagainst departures from normality, which means that the distribution of sample differences must be very close to a normal distribution.

c.If we want to use a confidence interval to test the claim that\({{\bf{\mu }}_{\bf{d}}}{\bf{ < 0}}\)with a 0.01 significancelevel, the confidence interval should have a confidence level of 98%.

d.The methods of this section can be used with annual incomes of 50 randomly selected attorneysin North Carolina and 50 randomly selected attorneys in South Carolina.

e.With ten matched pairs of heights, the methods of this section require that we use n= 20.

Short answer

a. The statement is true.

b. The statement is false.

c. The statement is true.

d. The statement is false.

e. The statement is false.

Step-by-step solution

Explain decision rules for the hypothesis test

a.

In case of matched pairs of heights, the p-value and critical value approaches are used to make a decision about the null hypothesis.

The values are computed on the same test statistic value and the critical region of same distribution. Simultaneously, the confidence interval on the corresponding level of confidence can be used to make the same decision.

Therefore, usually thethree methods p-value, critical value and confidence interval takes same distribution and standard error.

Therefore, given statement is true.

Explain requirement of the t-test.

b.

In hypothesis test, t-test is used when the data follows normal distribution. The requirement of t-test says that the data should follow normal distribution. But in paired t-test the property says that, it isrobustagainst departures from normality.

The phrase robust against departures from normality implies that the requirement for normal distribution in case of matched pair is loose (not strict).

Therefore, given statement is false.

Explain the selection of confidence interval

c.

The confidence interval percentage changes based on the tail of the test.

According to table 8-1 for two tailed test,\(98\% \)confidence level is used for\(\alpha = 0.02\)but for one tailed test, for the level of significance\({\bf{\alpha = 0}}{\bf{.01}},\)98% confidence level should be used.

Therefore, given statement is true.

Explain the difference between independent sample and dependent sample

d.

The variables are said to be independent if the given variables are not related to each other, or one variable do not influence the other. The variables are matched pairs when the samples of subjects are taken in two different situations.

In this case,50 randomly selected attorneys in North Carolina and 50 randomly selected attorneys in South Carolina different independent samples. They are not related to each other. Hence it cannot be used for matched pairs.

Therefore, given statement is false

Explain the selection of sample size.

e.

In matched pairs there will be two dependent variables which means the same sample is recorded in two different situation.

In ten matched pair of heights, the sample is only 10, but not 20 because they are matched, which means the 10 sample heights are given in two different situations. Hence the sample size (n) will be only 10.

Hence the given statement is false.