Question 1: Significance Tests In a test of hypotheses, a researcher used the le

Question

Question 1: Significance Tests In a test of hypotheses, a researcher used the level of significance a-0.05.Based on a random sample, she obtained a P-value of 0.052. Which of the following is strictly true for this level of significance and conditions? Select one: a. There is some evidence against H0° and a study using a larger sample size may be worthwhile. b. The data suggest that further investigation of the hypotheses (using another sample and study) will not be significant at the a 0.05 significance level .Her sample provides little to no evidence for O d. She may conclude that Ho is true because her sample provdes evidrce to pport it. Can brainwaves be used to measure job aptitude? During the 1980s, a psychologist tried to use brainwave measurements to identity U.S. Navy recruits who are good at using a rifle. Several times each year, batches of data were analyzed. Each batch of data compared various brainwave measurements with rifle-shooting performance scores for a group of recruits. The psychologist was looking for evidence of a relationship between brainwave measures and shooting skill During 1990, he analyzed 34 of these batches. In 32 of those batches, there was no evidence of association, but the other two batches were statistically significant (at level of significance a 0.05) in demonstrating a relationship between brainwaves and shooting skill. Based on this, which of the following is true? Select one: a. The psychologist should toss out the 32 batches of data that failed to demonstrate an association between brainwaves and shooting skill and keep the two batches that do demonstrate an association. After all, the grant that funds such research and pays the psychologist's salary needs to be renewed. O b. There's little evidence of an association. After all, since we're testing each batch of data at the a -0.05 level of significance, by chance alone 1 in 20 batches would demonstrate an association even if there really isn't one. This explains the two "good batches the psychologist observed. c. The psychologist should just pick one of the data sets (at random) and base his analysis on that d. All of the above. A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes lP·0287) This means Select one: athe GPAs for male and female scholarship athletes are identical, except for 28.7% of the athletes. b. the maximum difference in GPAs between male and female scholarship athletes is 0.287 adfference in GPAs between male and female scholarship athletes large as that observed inte sample is 0287 d. the chance that a pair of randomly chosen male and female scholarship athletes would have a significant c.if thero really is no difference in moan GPA for male and female sclolarship athletes, the probablity of ob vrg difference in GPAs is 0.287 Suppose in a test of hypotheses, the researcher observes data and computes a P-value of P that these data are statistically significant. Since the P-value is so smal, 0.0001. He then decldes a, the rusearch er has proven the null hypothesis is b. the rosearchor has strong evidence that the claim as stated in the aiternative hypothosis is true, but there is no indication of how big the offect irs e. the rosearcher may now conclude that not only is there an effect, but the eftect must be very large. d, thereanan her should conclude that terrible "mors wore made in colecting dataAfter ..Avak sch as P 00001 means that if the rull hypothesis is true, sample ikn this e was vnamy mpoositie to occur bydwoe

Explanation / Answer

Solution

Back-up Theory

Meaning and Interpretation of p-value

p-value represents the probability of getting the observed test statistic value when the null hypothesis is true.

If p-value is greater than the given level of significance, the null hypothesis is accepted and if it is less than the given level of significance, the null hypothesis is rejected which in turn implies that the Alternative is true.

The difference between the level of significance and p-value would only indicate how strong or weak, as the case may be, the evidence is in favour or against the null hypothesis.

p-value, thus, does not quantify the effect of the claim under null hypothesis or alternative, as the case may be.

Now to work out the solution,

Part (a)

p-value 0.052

0.052 being greater than the given level of significance, 0.05, null hypothesis H0 is accepted. Implies that there is evidence to suggest that H0 is true. But, one cannot say how strong the effect is. Thus, correct answer is: option d ANSWER

Part (b)

Brainwave vs Shooting Skill

5% level of significance only implies that there is 5% chance of rejecting the null hypothesis whenit is true. in the given case, in 32 out of 34 batches, null hypothesis has been rejected, which is very high.

This implies that the rejection cannot be chance. Hence

Option b ANSWER

Part (c)

Scholarship Athletes

Here the chance of getting the observed test statistic value is 0.287 if the null hypotheis is true.Implies that the chance of the null hypothesis being true is quite high. Hence

Option c ANSWER

Part (d)

p-value 0.0001 being very small, null hypothesis is rejected. Implies there is strong evidence to suggest that the claim under the null hypotheis is not true or claim under H1 is is true. But, it does not quantify the how large the effect of H1 is. Hence

Option b ANSWER

DONE

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.