1.) Giving a test to a group of students, the grades and gender are summarized b
ID: 3069673 • Letter: 1
Question
1.) Giving a test to a group of students, the grades and gender are summarized below
If one student is chosen at random, find the probability that the student was male OR got an "B". Round your answer to 4 decimal places.
2.)
A CBS News poll involved a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.
If we randomly select one of the adults who participated in this study, compute: (round to four decimal places)
P(worse|Democrat) =
P(Democrat|worse) =
3.)
A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 89 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 43 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 46 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below (Allais, 2011).
(round answers to 2 decimal places)
a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? %
b) What percent of patients in the control group were pain free after 24 hours? %
c) At first glance, does acupuncture appear to be an effective treatment for migraines? Explain your reasoning.
no, because more than half of the individuals in the treatment group still experience pain 24 hours later
yes, because a higher percentage of individuals in the treatment group were pain-free after 24 hours
no, because there were fewer people in the treatment group
yes, because more individuals in the treatment group were pain-free after 24 hours
d) Do the data provide convincing evidence that there is a real pain reduction for those patients in the treatment group? Or do you think that the observed difference might just be due to chance?
Yes, 23% is much higher than 4%
It is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample
4.)
You roll two six-sided fair dice.
a. Let A be the event that either a 4 or 5 is rolled first followed by an even number.
P(A) = Round your answer to four decimal places.
b. Let B be the event that the sum of the two dice is at most 5.
P(B) = Round your answer to four decimal places.
5.)
An experiment consists of first rolling a die and then tossing a coin:
a. How many elements are there in the sample space?
b. Let A be the event that either a 3 or 4 is rolled first, followed by landing a head on the coin toss.
P(A) = Present your answer as a decimal rounded to four decimal places.
Explanation / Answer
Solution :
1) From given table,
If one student is chosen at random, find the probability that the student was male OR got an "B" is,
= P(male) + P(B) - P(male and B)
= 44 / 64 + 30 / 64 - 17 / 64
= (44 + 30 - 17) / 64
= 57 / 64
= 0.8906
Probability = 0.8906
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