Question

(2 points) For each problem, select the best response. a) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H. :p=1.5, H iu > 1.5 and you obtain a P-value of 0.052. Which of the following is true? A. At the a = 0.05 significance level, you have proven that Ho is true B. This should be viewed as a pilot study and the data suggests that further investigation of the hypotheses will not be fruitful at the a= 0.05 significance level. C. There is some evidence against Ho, and a study using a larger sample size may be worthwhile. D. You have failed to obtain any evidence for Hq. b) Does 30 minutes of aerobic exercise each day provide significant improvement in mental performance? To investigate this issue, a researcher conducted a study with 150 adult subjects who performed aerobic exercise each day for a period of six months. At the end of the study, 200 variables related to the mental performance of the subjects were measured on each subject and the means compared to known means for these variables in the population of all adults. Nine of these variables were significantly better in the sense of statistical significance) at the a = 0.05 level for the group that performed 30 minutes of aerobic exercise each day as compared to the population as a whole, and one variable was significantly better at the a= 0.01 level for the group that performed 30 minutes of aerobic exercise each day as compared to the population as a whole. It would be correct to conclude A. that these results would have provided very good statistical evidence that 30 minutes of aerobic exercise each day provides some improvement in mental performance if the number of subjects had been larger. It is premature to draw statistical conclusions from studies in which the number of subjects is less than the number of variables measured. OB. that there is very good statistical evidence that 30 minutes of aerobic exercise each day provides improvement for the variable that was significant at the a= 0.01 level. We should be somewhat cautious about making claims for the variables that were significant at the a= 0.05 level. C. that there is very good statistical evidence that 30 minutes of aerobic exercise each day provides some improvement in mental performance. D. none of the above.

Answer 1

1. Here the null hypothesis is Ho: µ=1.5 w.r.to Ha: µ>15. This is a right tailed test. In the problem sample size is not mentioned. We are testing at 5% level of significance. The obatained p value is .052. As we are testing at 5% level of significance and p value is .052 we may conclude that the null hypothesis is accepted at 5% level of significance. But sample size is not mentioned and Ho is also being accepted at marginal  p value of 0.052, which is very near to .05.

(i) the first option is mathematically correct but is is not acceptable as p=.052 which is very near to α=0.05. So further analysis may give different results.

(ii) This study can be seen as a pilot study but further investigation may result to conclusive results. So this option is not correct.

(iii) This option is correct, as there is some evidence against Ho as p value is marginal .052. A study using larger sample may give fruitful results.

(iv) This option is also not correct as Ho is accepted with very less statistical signifiacnce of p=.052 so there is no evidence for Ha is not correct.

Option (iii) is correct.

2. Here the test is done at 5% level of significance, with 150 adults but 200 variables related to the mental performance of the subject. As the variables to be tested is so large the sample size should be large to give any conclusive result.

(i) This option is correct as it is premature to draw any conclusion beacause number of subjects is less than the variables used.

(ii) The 9 variables may be signifiacant at 5% level of significance and one at 1% level of significance, since the number of subjects is less than the variables used so the results are inconclusive.

(iii) There is good statistical evidence to accept the hypothesis is incorrect since number of subjests is less than the variables used.

(iv) it is not a correct option

Option (i) is correct