In each of the following situations explain what is wrong and why. (a) A researc
ID: 3152447 • Letter: I
Question
In each of the following situations explain what is wrong and why.
(a) A researcher wants to test
H0: x1 = x2
versus the two-sided alternative
Ha: x1 x2.
The null hypothesis H0 should indicate that the two means are not equal.The alternative hypothesis Ha should indicate that
x1 x2
. The null hypothesis (but not the alternative hypothesis) should involve 1 and 2 (population means) rather than
x1 and x2
(sample means).Hypotheses should involve 1 and 2 (population means) rather than
x1 and x2
(sample means).This alternative hypothesis indicates a one-sided hypothesis instead of a two-sided hypothesis.
(b) A study recorded the IQ scores of 50 college freshmen. The scores of the 24 males in the study were compared with the scores of all 50 freshmen using the two-sample methods of this section.
The samples are too small to be used for hypothesis testing.The sample sizes are too different to be used for hypothesis testing; we would need to have more males in the sample. A two-sample method is not appropriate in this situation.The samples are too large to be used for hypothesis testing.The samples are not independent; we would need to compare the 24 males to the 26 females.
(c) A two-sample t statistic gave a P-value of 0.93. From this we can reject the null hypothesis with 90% confidence.
We can reject the null hypothesis, but with less than 90% confidence.We can reject the null hypothesis, but with more than 90% confidence. We need the P-value to be negative to reject H0.A P-value of this size is impossible.We need the P-value to be small to reject H0.
(d) A researcher is interested in testing the one-sided alternative
Ha: 1 < 2.
The significance test gave
t = 2.25.
Since the P-value for the two-sided alternative is 0.04, he concluded that his P-value was 0.02.The alternative hypothesis should state that
Ha: 1 2.
Assuming the researcher computed the t statistic using
x1 x2,
a positive value of t does not support Ha. A one-sided alternative should never be used.A t statistic of this size should have a much larger P-value associated with it.The alternative hypothesis should state that
Ha: 1 2.
Explanation / Answer
(a)The hypotheses are wrong.
The null hypothesis (but not the alternative hypothesis) should involve 1 and 2 (population means) rather than x1 and x2
H0:mu1=mu2
Ha:mu1mu2
(b) The samples are not independent; we would need to compare the 24 males to the 26 females.
(c) We need the P-value to be small to reject H0.
(d) The alternative hypothesis should state that
Ha: 1 2.
Assuming the researcher computed the t statistic using
x1 x2,
a positive value of t does not support Ha.
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