Question

Suppose we have taken independent, random samples of sizes n1 = 8 and n2 = 8 from two normally distributed populations having means µ1 and µ2, and suppose we obtain x¯1 = 227, x¯2 = 190 , s1 = 6, s2 = 6. Use critical values to test the null hypothesis H0: µ1 − µ2 < 27 versus the alternative hypothesis Ha: µ1 − µ2 > 27 by setting α equal to .10, .05, .01 and .001. Using the equal variance procedure, how much evidence is there that the difference between µ1 and µ2 exceeds 27? (Round your answer to 3 decimal places.) t = H0 at α = 0.1, 0.05, and, 0.01, evidence.

Answer #1

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...

Suppose we have taken independent, random samples of sizes
n1 = 7 and n2 = 8 from two normally
distributed populations having means µ1 and
µ2, and suppose we obtain x¯1 = 229x¯1 =
229, x¯2 = 190x¯2 = 190, s1 = 6, s2 =
6. Use critical values to test the null hypothesis
H0: µ1 −
µ2 < 28 versus the alternative hypothesis
Ha: µ1 −
µ2 > 28 by setting α equal to .10, .05, .01
and .001....

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 = 240 , x¯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...

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...

Suppose a sample of 49 paired differences that have been
randomly selected from a normally distributed population of paired
differences yields a sample mean of d⎯⎯=5.9 and a sample standard
deviation of sd = 7.4. (a) Calculate a 95 percent confidence
interval for µd = µ1 – µ2. Can we be 95 percent confident that the
difference between µ1 and µ2 is greater than 0? (Round your answers
to 2 decimal places.) Confidence interval = [ , ] ; (b)...

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.

In order to compare
the means of two normal populations, independent random samples are
taken of sizes n1 = 400 and n2 = 400. The
results from the sample data yield:
Sample 1
Sample 2
sample mean = 5275
sample mean = 5240
s1 = 150
s2 = 200
To test the null
hypothesis H0: µ1 - µ2 = 0 versus
the alternative hypothesis Ha: µ1 -
µ2 > 0 at the 0.01 level of significance, the most
accurate statement...

(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...

Given the information below that includes the sample size (n1
and n2) for each sample, the mean for each sample (x1 and x2) and
the estimated population standard deviations for each case( σ1 and
σ2), enter the p-value to test the following hypothesis at the 1%
significance level :
Ho : µ1 = µ2
Ha : µ1 > µ2
Sample 1
Sample 2
n1 = 10
n2 = 15
x1 = 115
x2 = 113
σ1 = 4.9
σ2 =...

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...

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