(1) A researcher wants to test H0: x1 = x2versus the two-sided alternative Ha: x1 ≠x2.
(a) This alternative hypothesis indicates a one-sided hypothesisinstead of a two-sided hypothesis.
(b) The alternative hypothesis Ha should indicate that x1 ≥ x2.
(c)The null hypothesis (but not the alternative hypothesis)should involve μ1 and μ2(population means) rather than x1 andx2 (sample means).
(d) Hypotheses should involve μ1 andμ2 (population means) rather thanx1 and x2 (samplemeans).
(e) The null hypothesis H0 should indicatethat the two means are not equal.
(2) A study recorded the IQ scores of 50college freshmen. The scores of the 24 males in the study werecompared with the scores of all 50 freshmen using the two-samplemethods of this section.
(a)The samples are too large to be used for hypothesistesting.
(b)The samples are not independent; we would need to compare the24 males to the 26 females.   Â
(c) The samples are too small to be used for hypothesistesting.
(d)The sample sizes are too different to be used for hypothesistesting; we would need to have more males in the sample.
(e)A two-sample method is not appropriate in this situation.
(3)A two-sample t statistic gave aP-value of 0.93. From this we can reject the nullhypothesis with 90% confidence.
(a)We can reject the null hypothesis, but with less than 90%confidence.
(b) We need the P-value to be small to rejectH0.   Â
(c) We can reject the null hypothesis, but with more than 90%confidence.
(d) We need the P-value to be negative to rejectH0.
(e)A P-value of this size is impossible.
(4)A researcher is interested in testing theone-sided alternative Ha:μ1 < μ2. Thesignificance test gave t = 2.25. Since theP-value for the two-sided alternative is 0.04, heconcluded that his P-value was 0.02.
(a) The alternative hypothesis should state thatHa: μ1 ≠μ2.
(b) A one-sided alternative should never beused.   Â
(c) The alternative hypothesis should state thatHa: μ1 ≤μ2.
(d) Assuming the researcher computed the t statisticusing x1 − x2,a positivevalue of t does not support Ha.
(e)A t statistic of this size should have a much largerP-value associated with it.
