Question
In: Statistics and Probability
5. Suppose that researchers study a sample of 50 people and nd that 10 are left-handed....
5. Suppose that researchers study a sample of 50 people and nd that 10 are left-handed.
(a) Find a 95% confidence interval for the population proportion that is left-handed.
(b) What would the confidence interval be if the researchers used the Wilson value ~p instead?
(c) Suppose that an investigator tests the null hypothesis that the population proportion is 18% against the alternative that it is less than that. If = 0:05 then nd the critical value ^pc. Using ^p as the sample estimate, would the investigator reject the null?
(d) Suppose that researchers are using this critical value but, unbeknownst to them, the true, population proportion is 0.16. Find the power of the test.
Solutions
Expert Solution
It is a problem of one sample proportion test with a left tail alternative. Here we also find the confidence interval. All the required theoretical explanations are given in the solution.
orchestra answered 1 year agoRelated Solutions
5. Suppose that researchers study a sample of 50 people and find that 10 are left-handed....
5. Suppose that researchers study a sample of 50 people and find
that 10 are left-handed. (a) Find a 95% confidence interval for the
population proportion that is left-handed.
(b) What would the confidence interval be if the researchers
used the Wilson value p ̃ instead?
(c) Suppose that an investigator tests the null hypothesis that
the population proportion is 18% against the alternative that it is
less than that. If α = 0.05 then find the critical value pˆc....
5. Suppose that researchers study a sample of 50 people and find that 10 are left-handed....
5. Suppose that researchers study a sample of 50 people and find
that 10 are left-handed. (a) Find a 95% confidence interval for the
population proportion that is left-handed. (b) What would the
confidence interval be if the researchers used the Wilson value ̃p
instead? (c) Suppose that an investigator tests the null hypothesis
that the population proportion is 18% against the alternative that
it is less than that. If α = 0.05 then find the critical value ˆpc.
Using...
Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a)...
Suppose that researchers study a sample of 50 people and find
that 10 are left-handed.
(a) Find a 95% confidence interval for the population proportion
that is left-handed.
(b) What would the confidence interval be if the researchers
used the Wilson value ~p instead?
(c) Suppose that an investigator tests the null hypothesis that
the population proportion is 18% against the alternative that it is
less than that. If = 0:05 then nd the critical value ^pc. Using ^p
as...
Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a)...
Suppose that researchers study a sample of 50 people and
find that 10 are left-handed.
(a) Find a 95% confidence interval for the population
proportion that is left-handed.
(b) What would the confidence interval be if the
researchers used the Wilson value ̃p instead?
(c) Suppose that an investigator tests the null
hypothesis that the population proportion is 18% against the
alternative that it is less than that. If α = 0.05 then find the
critical value ˆpc. Using ˆp...
. Approximately 10% of all people are left-handed, then the rest of people are right-handed. Consider...
. Approximately 10% of all people are left-handed, then the rest
of people are right-handed. Consider a group of 15 people, answer
the following question: (You cannot use the binomial table for this
problem) (a) State the random variable ?. (2 points) (b) Explain
why this is a binomial experiment. There should be 4 conditions to
check. (State the probability of left-handed people ?, the possible
outcomes, and the number of trials ? in the conditions.) (4 points)
(c) Find...
Do left-handed people live shorter lives than right-handed people? A study of this question examined a...
Do left-handed people live shorter lives than right-handed
people? A study of this question examined a sample of 949 death
records and contacted next of kin to determine handedness. Note
that there are many possible definitions of "left-handed." The
researchers examined the effects of different definitions on the
results of their analysis and found that their conclusions were not
sensitive to the exact definition used. For the results presented
here, people were defined to be right-handed if they wrote, drew,...
Assume that 73% of people are left-handed. If we select 5 people at random, find the...
Assume that 73% of people are left-handed. If we select 5 people
at random, find the probability of each outcome described below,
rounded to four decimal places:
a. There are some lefties (≥ 1) among the 5 people.
b. There are exactly 3 lefties in the group.
c. There are at least 4 lefties in the group.
d. There are no more than 2 lefties in the group.
e. How many lefties do you expect?
f. With what standard deviation?
Assume that 37% of people are left-handed. If we select 5 people at random, find the...
Assume that 37% of people are left-handed. If we select 5 people
at random, find the probability of each outcome described below,
rounded to four decimal places: a. There are some lefties ( ≥ 1)
among the 5 people. b. There are exactly 3 lefties in the group. c.
There are at least 4 lefties in the group. d. There are no more
than 2 lefties in the group. e. How many lefties do you expect? f.
With what standard...
Assume that 51% of people are left-handed. If we select 5 people at random, find the...
Assume that 51% of people are left-handed. If we select 5 people
at random, find the probability of each outcome described below,
rounded to four decimal places:
a. There are some lefties (≥ 1) among the 5 people.
b. There are exactly 3 lefties in the group.
c. There are at least 4 lefties in the group.
d. There are no more than 2 lefties in the group.
e. How many lefties do you expect?
f. With what standard deviation?
Assume that 57% of people are left-handed. If we select 5 people at random, find the...
Assume that 57% of people are left-handed. If we select 5 people
at random, find the probability of each outcome described below,
rounded to four decimal places:
a. There are some lefties (≥ 1) among the 5 people.
b. There are exactly 3 lefties in the group.
c. There are at least 4 lefties in the group.
d. There are no more than 2 lefties in the group.
e. How many lefties do you expect?
f. With what standard deviation?
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