Question

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.

Answer #1

In a completely randomized experimental design, three brands of
paper towels were tested for their ability to absorb water.
Equal-size towels were used, with four sections of towels tested
per brand. The absorbency rating data follow.
Brand
x
y
z
91
100
84
99
95
88
89
93
90
85
104
74
At a 0.05 level of significance, does there appear to be a
difference in the ability of the brands to absorb water?
State the null and alternative hypotheses....

In a completely randomized experimental design, three brands of
paper towels were tested for their ability to absorb water.
Equal-size towels were used, with four sections of towels tested
per brand. The absorbency rating data follow.
Brand
x
y
z
90
99
83
100
97
87
87
93
90
95
99
72
At a 0.05 level of significance, does there appear to be a
difference in the ability of the brands to absorb water?
State the null and alternative hypotheses....

In a completely randomized experimental design, three brands of
paper towels were tested for their ability to absorb water.
Equal-size towels were used, with four sections of towels tested
per brand. The absorbency rating data follow.
Brand
x
y
z
92
98
84
101
95
87
88
93
88
87
102
77
At a 0.05 level of significance, does there appear to be a
difference in the ability of the brands to absorb water?
State the null and alternative hypotheses....

Medical researchers interested in determining the relative
effectiveness of two different drug treatments on people with a
chronic mental illness established two independent test groups. The
first group consisted of 7 people with the illness, and the second
group consisted of 12 people with the illness. The first group
received treatment 1 and had a mean time until remission of 199
days, with a standard deviation of 6 days. The second group
received treatment 2 and had a mean time...

Makeup artists evaluated two brands of liquid eye liner for wear
time (the amount of time in hours before the appearance on the eyes
is no longer noticeable) using 45 people. Descriptive statistics
from the paired samples t-test results are as follows: d̄ = ?, sd =
?, nd = 45. The 95% confidence interval for the mean paired
difference (Luxury Brand – Kylie Cosmetics Brand) is (1.4 ,
2.6).
Find d̄ =

Three different brands of car batteries, each having a 42 month
warranty, were included in a study of battery lifetime. A random
sample of batteries of each brand was selected, and lifetime, in
months, was determined.
An analysis of variance was conducted and the p-value was 0.053.
The hypothesis that all mean lifetimes are the same was retained at
the 5% level.
Multiple comparisons of the means were also carried out with the
following (somewhat contradictory) findings:
The Tukey's 95%...

Two researchers conducted a study in which two groups of
students were asked to answer 42 trivia questions from a board
game. The students in group 1 were asked to spend 5 minutes
thinking about what it would mean to be a professor, while the
students in group 2 were asked to think about soccer hooligans.
These pretest thoughts are a form of priming. The 200 students in
group 1 had a mean score of 22.3 with a standard deviation...

A company wants to examine the average operation time for a
process. Two methods were used. A random sample of 40 for the first
method gives an average mean time of 20.5 minutes with variance of
3 minutes. A random sample of 50 for the second method gives an
average mean time of 17.6 minutes with variance of 4 minutes. (Use
normal distribution with variance known)
Determine the 95% confidence interval for the difference
between the means
At alpha =0.05...

Two researchers conducted a study in which two groups of
students were asked to answer 42 trivia questions from a board
game. The students in group 1 were asked to spend 5 minutes
thinking about what it would mean to be a professor, while the
students in group 2 were asked to think about soccer hooligans.
These pretest thoughts are a form of priming. The 200 students in
group 1 had a mean score of 24.1 with a standard deviation...

Is the average time to complete an obstacle course longer when a
patch is placed over the right eye than when a patch is placed over
the left eye? Thirteen randomly selected volunteers first completed
an obstacle course with a patch over one eye and then completed an
equally difficult obstacle course with a patch over the other eye.
The completion times are shown below. "Left" means the patch was
placed over the left eye and "Right" means the patch...

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