Question

(S 11.1) Random samples of sizes n1 = 405 and n2 = 311 were taken from two independent populations. In the first sample, 120 of the individuals met a certain criteria whereas in the second sample, 131 of the individuals met the same criteria. Run a 2PropZtest to test whether the proportions are different, and answer the following questions.

What is the value of p?, the pooled sample proportion?.
**.3505586** Round your response to at least 3 decimal
places

Calculate the z test statistic, for testing the null hypothesis that the population proportions are equal.______________ Round your response to at least 2 decimal places.

Answer #1

The statistical software output for this problem is:

**Two sample proportion summary hypothesis
test:**

p_{1} : proportion of successes for population 1

p_{2} : proportion of successes for population 2

p_{1} - p_{2} : Difference in proportions

H_{0} : p_{1} - p_{2} = 0

H_{A} : p_{1} - p_{2} ? 0

**Hypothesis test results:**

Difference |
Count1 |
Total1 |
Count2 |
Total2 |
Sample Diff. |
Std. Err. |
Z-Stat |
P-value |
---|---|---|---|---|---|---|---|---|

p_{1} - p_{2} |
120 | 405 | 131 | 311 | -0.12492557 | 0.035974861 | -3.4725796 | 0.0005 |

Hence,

z test statistic = -3.47

Random samples of sizes n1 = 400 and n2 = 315 were taken from
two independent populations. In the first sample, 115 of the
individuals met a certain criteria whereas in the second sample,
123 of the individuals met the same criteria. Run a 2PropZtest to
test whether the proportions are different, and answer the
following questions. What is the value of p−, the pooled sample
proportion?Round your response to at least 3 decimal places. Number
Calculate the z test...

(S 11.3) Independent random samples of sizes n1 = 204
and n2 = 208 were taken from two populations. In the first
sample, 177 of the individuals met a certain criteria whereas in
the second sample, 179 of the individuals met the same
criteria.
Test the null hypothesis
H0:p1=p2versus the alternative
hypothesis HA:p1>p2.
Calculate the z test statistic, testing the null
hypothesis that the population proportions are equal.
_______________ Round your response to at least 2 decimal
places.
What...

Independent random samples of sizes n1 = 407 and n2 = 307 were
taken from two populations. In the first sample, 118 of the
individuals met a certain criteria whereas in the second sample,
163 of the individuals met the same criteria. Test the null
hypothesis H0:p1=p2versus the alternative hypothesis HA:p1≠p2. What
is the value of the z test statistic, testing the null hypothesis
that the population proportions are equal? Round your response to
at least 2 decimal places.

Suppose we have taken independent, random samples of sizes n1 =
7 and n2 = 6 from two normally distributed populations having means
µ1 and µ2, and suppose we obtain x¯1 = 240 , x¯2 = 208 , s1 = 5,
s2 = 5. Use critical values to test the null hypothesis H0: µ1 − µ2
< 22 versus the alternative hypothesis Ha: µ1 − µ2 > 22 by
setting α equal to .10, .05, .01 and .001. Using the...

Consider two independent random samples of sizes
n1 = 14 and n2 = 10, taken
from two normally distributed populations. The sample standard
deviations are calculated to be s1= 2.32 and
s2 = 6.74, and the sample means are
x¯1=-10.1and x¯2=-2.19, respectively. Using this information, test
the null hypothesis H0:μ1=μ2against the one-sided alternative
HA:μ1<μ2, using the Welch Approximate t Procedure (i.e.
assuming that the population variances are not equal).
a) Calculate the value for the t test statistic.
Round your...

Consider that two independent samples of sizes n1 and n2 are
taken from multivariate
normal populations with different mean vectors and same covariance
matrices. Give
maximum likelihood estimates of sample mean vectors and covariance
matrices. Also
discuss the distributional properties of the estimators.

Independent random samples of n1 = 100 and
n2 = 100 observations were randomly selected
from binomial populations 1 and 2, respectively. Sample 1 had 51
successes, and sample 2 had 56 successes.
b) Calculate the standard error of the difference in the two
sample proportions, (p̂1 − p̂2). Make sure to
use the pooled estimate for the common value of p. (Round
your answer to four decimal places.)
d)p-value approach: Find the p-value for the
test. (Round your answer...

Independent random samples of
n1 = 900 and n2 = 900
observations were selected from binomial populations 1 and 2,
and
x1 = 120
and
x2 = 150
successes were observed.
(a)
What is the best point estimator for the difference
(p1 − p2)
in the two binomial proportions?
p̂1 − p̂2
n1 −
n2
p1 − p2
x1 − x2
(b)
Calculate the approximate standard error for the statistic used
in part (a). (Round your answer to three decimal...

Independent random samples of
n1 = 600
and
n2 = 440
observations were selected from binomial populations 1 and 2,
and
x1 = 334
and
x2 = 378
successes were observed.
(a) Find a 90% confidence interval for the difference
(p1 − p2) in the two
population proportions. (Round your answers to three decimal
places.)
to
(b) What assumptions must you make for the confidence interval to
be valid? (Select all that apply.)
independent samples
random samples
nq̂ > 5...

Suppose we have taken independent, random samples of sizes
n1 = 7 and n2 = 7 from two
normally distributed populations having means
µ1 and µ2, and suppose we
obtain x⎯⎯1= 240x¯1 = 240 , x⎯⎯2=210x¯2 = 210 ,
s1 = 5, s2 = 6. Use
critical values to test the null hypothesis H0:
µ1− µ2 < 20 versus the
alternative hypothesis Ha:
µ1 − µ2 > 20 by setting
α equal to .10, .05, .01 and .001. Using the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 12 minutes ago

asked 21 minutes ago

asked 24 minutes ago

asked 25 minutes ago

asked 40 minutes ago

asked 46 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago