Biostatistics: 1288831

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1. ALL of the above
2. BOTH tests have degrees of freedom of N – 1.
3. The variable measured is approximately normally distributed.
4. 1
5. ALL of the above
6. The probability that the alternative hypothesis is true is .95.
7. all population means are the same
8. The result is never statistically significant.
9. the sample size and the number of groups
10. F obtained, T obtained
11. accept the null hypothesis
12. Random sampling of cases must have taken place, There is homogeneity of variance,
13. the difference between the population means
14. as X increases, Y decreases
15. .15
16. Positive, linear, imperfect
17. 0.75

1. Proportion of shoulder pain explained by shoulder range of motion = 0.4*0.4 = 0.16 or 16%

Proportion of shoulder pain explained by shoulder injury = 0.2*0.2 = 0.04 or 4%

It may be concluded that proportion of variance in shoulder pain explained by shoulder range of motion is four time that explained by shoulder injury.

1. Paired t test would be most appropriate for comparing the means of the two populations.
2. There is no significant different between the means of the two populations.
3. The mean of population 1 is significantly greater than the corresponding mean of population 2.
4. Full range of correlation coefficient is from -1 to +1.
5. All F tests are non-directional since the null hypothesis assumes that means of all groups is the same and the alternative hypothesis indicates that atleast one group has non-equal mean. The alternative hypothesis has no direction component captured using “>” or “<” sign which indicates the non-directional nature of this test.
6. Hypothesis testing is based on the logic of determining of the underlying observations indicate any significant pattern. This is usually captured by the alternative hypothesis. Null hypothesis indicates the condition where the observations are non-significant. If the observations are significant, then null hypothesis which serve as reference would be rejected implying acceptance of alternative hypothesis.
7. With regards to conducting multiple t tests, it is noteworthy that there is a chance of doing Type 1 error which would be 5% assuming this is the significance level. As multiple comparisons are made, the Type 1 error probability continues to rise with roughly 5% in each of the tests. Thus, if three comparisons are made, the error chances can be approximately 15%. This situation can be avoided with the use of ANOVA which serves the same purpose but at a Type 1 error of only 5%. Thus, ANOVA is preferable over multiple t tests for comparing means.
8. A single estimate of standard deviation is required so as to estimate the standard error which is a key input in the estimation of the test statistic which further is used for perform hypothesis testing.
9. It may be concluded that there is a significant difference in the availability of ventilators per capita is significantly higher in New York as compared to California.

Question 28

1. Using symbols, write the directional alternative hypothesis:

H_a: µ_BMIPromotion < µ_BMIControl

• If alpha = .01 (1-tail), write the decision rule:

Reject the null hypothesis , if the test statistic is less than -1.86 (critical value)

• What is the value of the test statistic? *

Value of test statistics i.e. t statistic = -3.103

• Write the conclusion in the context of the study:

The conclusion is that the people with T2D who participated in the web-based health promotion program had lower BMI than the control group.

Question 28

1. What is the non-directional alternative hypothesis?

The average viral infections tend to be significantly different for atleast one of the four stress levels.

• Write the decision rule for alpha = .05:

Reject the null hypothesis if the test statistics is greater than the critical value of .

• What is the value of the test statistic?

F statistic = 7.74

• Write the conclusion in the context of the study:

It implies that average viral infection is not the same across the different levels of perceived stress.