Question

Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether mu 1μ1greater than>mu 2μ2 at the alphaαequals=0.10 level of significance for the given sample data. (b) Construct a 90% confidence interval about mu μ1−μ2.

Population 1 Population 2

n 23 | 19 |

x 46.2 | 45.1 |

s 5.1 | 13.4 |

Find the test statistic for the hypothesis test

Answer #1

a) We are testing, H0: u1= u2 vs H1: u1>u2

From the sample data, x1 - x2 = 1.1

S^2 = 22*5.1^2 + 18*13.4^2/23+19-2 = 95.1075

So the test statistic is: 1.1/√95.1075*(1/23 + 1/19) = 0.3639

The critical value of this test is at t 23+19-2 ie t40

So at alpha = 0.1 critical value is 1.303

Since our test statistic is less than the critical value, we have insufficient evidence to Reject H0. So we cannot conclude that u1>u2 at the 10% significance level.

b) 90% confidence interval for u1- u2 is given as:

1.1 +- 1.684*√95.1075*√1/23 + 1/19

=(-3.991, 6.191)

The confidence interval also gives us the same answer to the test, since it contains 0, it isn't statistically significant so we cannot Reject H0.

Use the given statistics to complete parts (a) and (b). Assume
that the populations are normally distributed.
(a) Test whether μ1>μ2 at the alphaαequals=0.01
level of significance for the given sample data.
(b) Construct a 90% confidence interval about μ1−μ2.
Population 1
Population 2
n
24
23
x overbarx
45.1
43.4
s
5.8
12.7

Use the given statistics to complete parts (a) and (b). Assume
that the populations are normally distributed.
(a) Test whether μ1>μ2
at the
alphaαequals=0.10
level of significance for the given sample data.(b) Construct a
90%
confidence interval about μ1−μ2.
Population 1
Population 2
n
24
6
x overbarx
49.6
44.1
s
7.4
14.1

Use the given statistics to complete parts (a) and (b). Assume
that the populations are normally distributed.
(a) Test whether mu 1 μ1 greater than > mu 2 μ2 at the alpha
α equals = 0.05 0.05 level of significance for the given sample
data.
(b) Construct a 95% confidence interval about mu 1 μ1 minus −
mu 2 μ2.
Population 1 Population 2
N 22 N 23
X 50.3 X 48.2
S 5.6 S 10.6
(a) Identify the...

Use the given statistics to complete parts (a) and (b). Assume
that the populations are normally distributed. (a) Test whether mu
1greater thanmu 2 at the alphaequals0.05 level of significance for
the given sample data. (b) Construct a 90% confidence interval
about mu 1minusmu 2. Population 1 Population 2 n 20 23 x overbar
50.7 46.9 s 4.8 12.8 (a) Identify the null and alternative
hypotheses for this test. A. Upper H 0: mu 1not equalsmu 2 Upper H
1:...

Provided below are summary statistics for independent simple
random samples from two populations. Use the pooled t-test and the
pooled t-interval procedure to conduct the required hypothesis
test and obtain the specified confidence interval.
x overbar 1x1equals=1414,
s 1s1equals=2.42.4,
n 1n1equals=1818,
x overbar 2x2equals=1515,
s 2s2equals=2.42.4,
n 2n2equals=1818
a. Two-tailed test,
alphaαequals=0.050.05
b.
9595%
confidence interval
a. First, what are the correct hypotheses for
a two-tailed test?
A.
Upper H 0H0:
mu 1μ1equals=mu 2μ2
Upper H Subscript aHa:
mu 1μ1not...

Given in the table are the BMI statistics for random samples of
men and women. Assume that the two samples are independent simple
random samples selected from normally distributed populations, and
do not assume that the population standard deviations are equal.
Complete parts (a) and (b) below. Use a 0.010.01 significance
level for both parts. Male BMI Female BMI muμ mu 1μ1 mu 2μ2 n 4545
4545 x overbarx 28.274128.2741 25.171825.1718 s 7.4101397.410139
4.3731854.373185

Consider the following hypothesis statement using
alphaαequals=0.10 and data from two independent samples. Assume the
population variances are equal and the populations are normally
distributed. Complete parts below.
H0: μ1−μ2 = 0 x overbar 1 = 14.8 x overbar 2 = 13.0
H1: μ1−μ2 ≠ 0 s1= 2.8 s2 = 3.2
n1 = 21 n2 = 15
a.) what is the test statistic?
b.) the critical values are
c.) what is the p value?

Given in the table are the BMI statistics for
random samples of men and women. Assume that the two samples are
independent simple random samples selected from normally
distributed populations, and do not assume that the population
standard deviations are equal. Complete parts (a) and (b) below.
Use a 0.01 significance level for both parts.
Male BMI
Female BMI
μ
μ1
μ2
n
50
50
x̄
27.7419
26.4352
s
8.437128
5.693359
a) Test the claim that males and females have...

Consider the following sample data and hypotheses. Assume that
the populations are normally distributed with
equal variances.
Sample Mean1 = 57
s1 =
21.5
n1 = 22
Sample Mean2 =
43
s2 =
15.2
n2 = 18
a. Construct the 90% Confidence Interval for the difference of
the two means.
H0: μ1 – μ2 = 5
HA: μ1 – μ2 ≠ 5
b. Using the hypotheses listed above, conduct the following
hypothesis test steps. Following the “Roadmap for Hypothesis
Testing”,...

Assume that both populations are normally distributed.
(a) Test whether
mu 1 not equals mu 2μ1≠μ2
at the
alpha equals 0.05α=0.05
level of significance for the given sample data.(b) Construct a
9595%
confidence interval about
mu 1 minus mu 2μ1−μ2.
Population 1
Population 2
n
1717
1717
x overbarx
10.810.8
14.214.2
s
3.23.2
2.52.5
(a) Test whether
mu 1 not equals mu 2μ1≠μ2
at the
alpha equals 0.05α=0.05
level of significance for the given sample data.
Determine the null and...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 33 minutes ago

asked 40 minutes ago

asked 42 minutes ago

asked 48 minutes ago

asked 50 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago