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Unformatted text preview: g a 99% conﬁdence interval, it is reasonable to conclude that the mean number of emergency
room admissions during a 24hour period is 21.
(d) A 99% conﬁdence interval is always more informative and preferable than a 95%
conﬁdence interval since we are more sure of the numbers we report.
(e) The margin of error is 1.225 and the sample mean is 19.8.
5. Researchers studying the eﬀectiveness of an antianxiety medication randomly sampled 100 patients
diagnosed with general anxiety disorder (GAD). Through random assignment half of the patients
received a placebo and the other half the antianxiety medication. The treatment was considered a
success if the patient experienced a reduction in their anxiety level. A 95% conﬁdence interval for the
diﬀerence between the proportion of success in the two groups (pmedication − pplacebo ) was (0.02, 0.24).
Based on this information, which of the following statements is (are) true?
(a) We are 95% conﬁdent that the true proportion of success among the population of
people who take the medication is 2% lower to 24% higher than the true proportion
of success among the population of people who take a placebo.
(b) 95% of random samples will produce a diﬀerence between 0.02 and 0.24.
(c) The 95% conﬁdence interval for (pplacebo − pmedication ) would be (0.24, 0.02).
(d) The 95% conﬁdence interval for (pplacebo − pmedication ) cannot be calculated without knowing the
actual sample proportions. 3 (e) We can conclude that the medication was eﬀective and the diﬀerence between the two sample
proportions was too large to plausibly be due to chance.
6. Since October 2008 chain restaurants in California are required to display calorie counts of each
menu item. Prior to menus displaying calorie counts, the average calorie intake of a diner at a CPK
restaurant was 1900 kcal. A nutritionist conducts a hypothesis test to see if there has been a signiﬁcant
decrease in the average calorie intake of CPK diners. Below is some information on the sample and
the hypothesis test:
x = 1806, s = 319, n = 30; t = −1.610, p − value = 0.06, α = 0.05
¯
Based on this information, which of the following statements is (are) true?
(a) The null hypothesis is µ = 1900 and the alternative hypothesis is µ = 1900.
(b) There is a 6% chance that the average calorie intake of the diners has remained at 1900 kcal.
(c) If in fact the average calorie intake of diners at a CPK has decreased, in 6% of random samples
of size 30 we would expect to observe an average calorie intake of 1806 kcal or less.
(d) If in fact the average calorie intake of diners at a CPK has not changed, in 6% of
random samples of size 30 we would expect to observe an average calorie intake of
1806 kcal or less.
(e) The diﬀerence between the sample mean of 1806 kcal and the null hypothesized mean
of 1900 kcal is due to natural sampling variation.
(f) The nutritionist fails to reject H0 and can prove that the average calorie intake has remained...
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This document was uploaded on 12/04/2013.
 Winter '13

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