Question

Company A claims that one of their drugs takes effect quicker than their competitor, Company B. To verify this claim, twenty volunteers were randomly assigned to take a drug from either Companies A or B. The following table shows the time (in minutes) the drug took each of the 20 volunteers to feel the effects:

Company A: 7.0 10.7 5.6 8.3 12.1 12.6 9.3 8.2 3.1 10.5

Company B 9.1 13.2 8.7 8.1 4.2 9.5 10.7 15.3 12.1 14.0

(a) Use the data collected, to determine if the claim from Company A is true at the 5% level of significance. You must state the null and alternative hypotheses, the name of the test or the test statistic, rejection criterion, decision and conclusion in terms of the original problem. Whenever necessary you may use the appropriate computer outputs given below. [7 marks]

Welch Two Sample t-test data:

time by company

t = -1.2534, df = 17.808, p-value = 0.1131

alternative hypothesis: true difference in means is less than 0

95 percent confidence interval:

-Inf 0.6725767 sample estimates:

mean in group A mean in group B

8.74 10.49

Welch Two Sample t-test data:

time by company

t = -1.2534, df = 17.808, p-value = 0.2263

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-4.68565 1.18565

sample estimates:

mean in group A mean in group B

8.74 10.49

(b) Will the conclusion in (a) be changed if the significance level was 10% instead? Explain your answer. [Note: you need not redo the test.] [2 marks]

(c) State the assumptions for the test used in (a). [3 marks]

(d) Check the assumptions you mentioned in (c). Whenever necessary, use the R Commander output on the next page. [3 marks]

(e) Explain why a paired t test would not be appropriate. [2 marks]

(f) To summarise the above data, a colleague produced two pie charts, one for Company A and one for Company B. Explain why the graph is inappropriate and suggest a suitable alternative graph. [3 marks]

Answer 1

a)

Since the P value is greater than the significance level, we fail to reject the null hypothesis. Hence we have no evidence to support the claim that one of their drugs takes effect quicker than their competitor, Company B.

b) P value for the one-tailed test is 0.1131.

Since the P-value is greater than significance level 0.1, we fail to reject the null hypothesis.

c) 1) The first assumption made regarding t-tests concerns the scale of measurement. The assumption for a t-test is that the scale of measurement applied to the data collected follows a continuous or ordinal scale.

2) The second assumption made is that of a simple random sample, that the data is collected from a representative, randomly selected portion of the total population.

3) The third assumption is the data, when plotted, results in a normal distribution, bell-shaped distribution curve.

4)The fourth assumption is a reasonably large sample size is used. A larger sample size means the distribution of results should approach a normal bell-shaped curve.

5) The final assumption is the homogeneity of variance. Homogeneous, or equal, variance exists when the standard deviations of samples are approximately equal.

d) The paired test would not be appropriate because in a paired sample t-test, each subject or entity is measured twice, resulting in pairs of observations.