Question

9.12 Suppose a 95% confidence interval for p1−p2 is (0.43, 0.51). A researcher wants to test H0∶p1−p2=0.5 versus Ha∶p1−p2≠0.5 at α=0.05 significance level. What is the p−value for this test?

Answer #1

TOPIC:Finding the p-value using the given confidence interval.

1. Consider this hypothesis test:
H0: p1 - p2 = 0
Ha: p1 - p2 > 0
Here p1 is the population proportion of “yes” of
Population 1 and p2 is the population proportion of
“yes” of Population 2. Use the statistics data from a simple random
sample of each of the two populations to complete the following:
(8 points)
Population 1
Population 2
Sample Size (n)
400
600
Number of “yes”
300
426
Compute the test statistic z.
What...

For a hypothesis test
of H0:p1 − p2 = 0 against the
alternative Ha:p1 − p2 ≠ 0, the
test statistic is found to be 2.2. Which of the following
statements can you make about this finding?
The result is
significant at both α = 0.05 and α = 0.01.
The result is
significant at α = 0.05 but not at α = 0.01.
The result is
significant at α = 0.01 but not at α = 0.05.
The result...

Conduct a test at the α=0.05 level of significance by
determining (a) the null and alternative hypotheses, (b) the test
statistic, and (c) the P-value. Assume the samples were obtained
independently from a large population using simple random sampling.
Test whether p 2p1>p2. The sample data are x1=118,
n1=254,x2=134, and n2=303. (a) Choose the correct null and
alternative hypotheses below.
A.
H0: p1=p2 Versus H1: p1
B.
H0: p1=p2 versus H1: p1≠p2
C.
H0: p1=0 versus H1: p1≠0
D.
H0:...

Conduct a test at the α=0.05 level of significance by
determining (a) the null and alternative hypotheses, (b) the test
statistic, and (c) the P-value. Assume the samples were obtained
independently from a large population using simple random sampling.
Test whether p1>p2. The sample data are x1=125, n1=243,x2=139,
and n2=307.
(a) Choose the correct null and alternative hypotheses
below.
A. H0: p1=p2 versus H1: p1>p2
B. H0: p1=0 versus H1: p1≠0
C. H0: p1=p2 Versus H1: p1
D.H0: p1=p2 versus...

1. Construct a confidence interval for p1-p2 at the given level
of confidence.
Group 1 X1= 110 N1 = 250
Group 2 X2=134 N2 = 298
Alpha = 95%
Confidence Interval p1-p2 = (_____, _____)
2.A sample size n = 50 is drawn from a normal population whose
standard deviation = 3.8. The sample mean = 20.41.
Construct a 95% confidence interval for mean

A researcher is conducting a randomized, placebo-controlled
experiment to test the hypotheses H0:p1=p2 versus Ha:p1>p2H_a:
p_1 > p_2Ha:p1>p2 where p1= the population proportion of
all patients given the new drug who are cured and p2=the population
proportion of all patients given the placebo who are cured. The
patients were randomly assigned to the two treatment groups in a 2
to 1 ratio, that is, twice as many patients were randomized to the
new treatment as were to the placebo group....

Question 3 This question concerns some concepts about
hypothesis testing and confidence interval. For each part below,
you must explain your answer.
(a) Suppose we are doing a one-sample t test at the 5% level of
significance where the hypotheses are H0 : µ = 0 vs H1 : µ > 0.
The number of observations is 8. What is the critical value? [2
marks]
(b) Suppose we are doing a hypothesis test and we can reject H0
at the...

Find the appropriate p-value to test the null hypothesis, H0: p1
= p2, using a significance level of 0.05.
n1 = 100 n2=200
x1= 38 x2= 40
A) .1610
B) .7718
C) .0412
D) .2130

Construct a confidence interval for p1−p2 at the given level of
confidence.
x1=26, n1=241, x2=30, n2=291, 95% confidence
The researchers are __% confident the difference between the two
population proportions, p1−p2, is between __ and __.

Construct a confidence interval for p1−p2 at the given level of
confidence.
x1=32, n1=272, x2=33, n2=306, 95% confidence.
____________________________________________________________________________
The researchers are __% confident the difference between the
two population proportions, p1−p2, is between __ and __.

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