Q1.Researchers were interested in determining the relative effectiveness of two different brands of eye drops in alleviating the symptoms of 'dry eye syndrome'. Forty subjects, who suffered from 'dry eye syndrome', were randomly assigned to receive either brand A or brand B of the eye-drops - 20 subjects to each brand. The eyedrops were administered to each subject and the time until symptoms returned was recorded for each subject. Based on the information provided, which of the following statement/s is necessarily TRUE for this study?
a. To conduct a hypothesis test of any differences between the mean times for the two brands, the appropriate degrees of freedom to use is 38.
b.This study is a matched pairs design.
c.The standard error of the difference between the mean time until symptoms reappear for the two brands is unaffected by whether or not we assume equal variability in times for each brand.
d. To construct a confidence interval estimate of the difference between the mean time until symptoms reappear for the two groups, the appropriate degrees of freedom to use is exactly 19.
Q2.A formal hypothesis test of μx - μy = 0 against μx - μy ≠ 0 concluded that there was a significant difference between the mean operating lifetimes for the two brands of products (p-value < 0.05). The findings were based on two random samples, one sample selected from each brand of product. For this test, which one of the following statements is FALSE?
a. The two models being compared in this hypothesis test are the single mean model and the separate means model.
b. The test would have been an independent samples test
c.Suppose the estimated variability in the possible estimates of μx - μy was incorrectly recorded as 7.3 when it should have been 17.3. Then the p-value calculated in the test using the wrong value is an overestimate of the p-value.
d.The standard deviation of the residuals from the separate means model must be smaller than the standard deviation of the residuals for the single mean model.
e. The varaibility in the two populations may or may not be equivalent.
Q3. A study was set up to explore the effects of high doses of antioxidants on macular degeneration. A control group (given no antioxidants) and a treatment group (administered large doses of antioxidants) were monitored over a period of time and the health of the macular was recorded. At the conclusion of the study, the researchers reported that antioxidants had a significant effect on macular health (p-value=0.04). They also reported that the power of the test, for alpha=0.05, is 0.8 when the effect size (difference in the population means for the two groups) was 6 units. From this information, which one of the following statements is likley to be FALSE?
A.If the true difference between the population means is 6 units, then 80% of the time the hypothesis test will conclude that antioxidants have an effect on macular health.
B. 5% of the time, the test will conclude that antioxidants have an effect on macular health, when, in fact, they don't.
C.95% of the time, the test will conclude that antioxidants are effective when, in fact, they aren't.
D.If the true difference between the population means is 6 units, then 20% of the time the hypothesis test will conclude that the two groups do not differ.
E.If the anitioxidants had no effect and this experiment were repeated many times then, four percent of the time we would observe a difference in means as extreme (or more extreme) as the one in our sample, just due to chance alone.
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