Question

The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo.

Characteristic*	New Drug	Standard Drug	Placebo	p
Age, years	45.2 (4.8)	44.9 (5.1)	42.8 (4.3)	0.5746
% Female	51%	55%	57%	0.1635
Annual Income, $000s	59.5 (14.3)	63.8 (16.9)	58.2 (13.6)	0.4635
% with Insurance	87%	65%	82%	0.0352
Disease Stage				0.0261
Stage I	35%	18%	33%
Stage II	42%	37%	47%
Stage III	23%	51%	20%

*Table entries and Mean (SD) or % Are there any statistically significant differences in the characteristics shown among the treatments? Justify your answer. Consider the test for differences in age among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only). Consider the test for differences in insurance coverage among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only). Consider the test for differences in disease stage among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only).

Answer 1

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Answer:

a).

The null and alternative hypotheses are stated below:

Null hypothesis: There is no significant difference in the characteristics shown among the treatments.

Alternative hypothesis: There is a significant difference in the characteristics shown among the treatments.

Consider, the significance level is 0.05.

From the given output, the p-values of characteristics % with insurance and Disease stage are 0.0352 and 0.0261 respectively.

Here, the p-values of both characteristics are less than the level of significance. We can reject the null hypothesis at the 0.05 significance level. Thus, there is a statistically significant difference in the characteristics shown among the treatments.

b)

The null and alternative hypotheses are stated below:

The formula for test statistic is as follows:

c)

The null and alternative hypotheses are stated below:

The formula for test statistic is as follows:

d)