Consumers can purchase nonprescription medications at food stores, mass merchandise stores such as
Target and Wal-Mart, or pharmacies. About 45% of consumers make such purchases at pharmacies.
What accounts for the popularity of pharmacies, which often charge higher prices?
A study examined consumers’ perceptions of overall performance of the three types of stores, using a
long questionnaire that asked about such things as “neat and attractive store,” “knowledgeable staff,”
and “assistance in choosing among various types of nonprescription medication.” A performance score
was based on 27 such questions. The subjects were 194 people chosen at random from the Indianapolis
telephone directory. Here are the means and standard deviations of the performance scores for the
sample.
Store type x s
Food stores 18.68 25.04
Mass merchandisers 32.11 33.21
Pharmacies 48.55 35.68
We do not know the population standard deviations, but a sample standard deviation s from so large a
sample is usually close to σ. Use s in place of the unknown σ in this exercise.
(a) What population do you think the authors of the study want to draw conclusions about?
sick people
citizens of Indianapolis
pharmacies
the American public
consumers
What population are you certain they can draw conclusions about?
citizens of Indianapolis
pharmacies
cons
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Mass merchandisers
Pharmacies
(c) Based on these confidence intervals, are you convinced that consumers think that pharmacies
offer higher performance than the other types of stores? (In Chapter 12, we will study a
statistical method for comparing means of several groups.)
Yes, the pharmacy interval is well above the others.
Yes, the mass merchandiser interval is well above the others.
Yes, the food store interval is well below the others.
No, there is no clear evidence of a significant difference.
,
,
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2. –/10 pointsMIntroStat9 7.E.034.
Since previous studies have reported that elite athletes are often deficient in their nutritional intake (for
example, total calories, carbohydrates, protein), a group of researchers decided to evaluate Canadian
high-performance athletes. A total of from eight Canadian sports centers participated
in the study. One reported finding was that the average caloric intake among the was
2403.7 kilocalories per day (kcal/d). The recommended amount is 2811.5 kcal/d.
For one part of the study, athletes from eight Canadian sports centers were surveyed.
Their average caloric intake was 3077.0 kilocalories per day (kcal/d) with a standard deviation of 986.0.
The recommended amount is 3422.2. Is there evidence that Canadian high-performance male athletes
are deficient in their caloric intake?
(a) State the appropriate
State the appropriate
(b) Carry out the test. (Round your answer for t to three decimal places.)
Give the degrees of freedom.
Give the P-value. (Round your answer to four decimal places.)
State your conclusion.
We have sufficient evidence to conclude that Canadian high-performance male athletes
are deficient in their calorie intake.
We do not have sufficient evidence to conclude that Canadian high-performance male
athletes are deficient in their calorie intake.
n = 324 athletes
n = 201 women
n = 114 male
H0.
H0: μ > 3422.2
H0: μ ≤ 3422.2
H0: μ ≥ 3422.2
H0: μ = 3422.2
H0: μ ≠ 3422.2
Ha.
Ha: μ ≥ 3422.2
Ha: μ = 3422.2
Ha: μ > 3422.2
Ha: μ ≠ 3422.2
Ha: μ < 3422.2
t =
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(c) Construct a 95% confidence interval for the daily average deficiency in caloric intake. (Round
your answers to one decimal place.)
, kcal/day
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3. –/10 pointsMIntroStat9 7.E.063.
Why do we naturally tend to trust some strangers more than others? One group of researchers decided
to study the relationship between eye color and trustworthiness. In their experiment the researchers
took photographs of 80 students (20 males with brown eyes, 20 males with blue eyes, 20 females with
brown eyes, and 20 females with blue eyes), each seated in front of a white background looking directly
at the camera with a neutral expression. These photos were cropped so the eyes were horizontal and at
the same height in the photo and so the neckline was visible. They then recruited 105 participants to
judge the trustworthiness of each student photo. This was done using a 10-point scale, where 1 meant
very untrustworthy and 10 very trustworthy. The 80 scores from each participant were then converted to
z-scores, and the average z-score of each photo (across all 105 participants) was used for the analysis.
Here is a summary of the results.
Eye color
Brown 40 0.55 1.68
Blue 40 −0.38 1.54
Can we conclude from these data that brown-eyed students appear more trustworthy compared to their
blue-eyed counterparts? Test the hypothesis that the average scores for the two groups are the same.
State the null and alternative hypotheses.
Report the test statistic, the degrees of freedom, and the P-value. (Round your test statistic to three
decimal places, your degrees of freedom to the nearest whole number, and your P-value to four decimal
places.)
t =
df =
P-value =
State your conclusion. (Use
We reject H0 and conclude that brown-eyed people seem more trustworthy according to this
experiment.
n x s
H0: μBrown ≠ μBlue
Ha: μBrown > μBlue
H0: μBrown = μBlue
Ha: μBrown > μBlue
H0: μBrown = μBlue
Ha: μBrown < μBlue
H0: μBrown = μBlue
Ha: μBrown ≠ μBlue
H0: μBrown ≠ μBlue
Ha: μBrown < μBlue
α = 0.05.)
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We do not reject H0 and can not conclude that brown-eyed people seem more trustworthy
according to this experiment.