Question

random sample of n1=17securities in Economy A produced mean returns of x̄ 1=5.8% with s1=2.5% while another random sample of n2=20 securities in Economy B produced mean returns of x̄ 2=4.6% with s2=2.2%.. At α =0.1 , can we infer that the returns differ significantly between the two economies?

Assume that the samples are independent and randomly selected
from normal populations with equal population variances ( σ
1^{2}= σ 2^{2})

T-Distribution Table

________________________________________

a. Calculate the test statistic.

t=

Round to three decimal places if necessary

________________________________________

b. Determine the critical value(s) for the hypothesis test.

+

Round to three decimal places if necessary

________________________________________

c. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

Answer #1

a.

*Test Statistics*

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

b.

*Rejection Region*

Based on the information provided, the significance level is α=0.1, and the degrees of freedom are df=35. In fact, the degrees of freedom are computed assuming that the population variances are equal.

Hence, it is found that the critical value for this two-tailed test is tc=1.690, for α=0.1 and df=35.

The rejection region for this two-tailed test is

c.

**Fail to Reject**

Since it is observed that ∣t∣=1.553≤tc=1.69, it is then
concluded that *the null hypothesis is not rejected.*

**Let me know in the comments if anything is not clear. I
will reply ASAP! Please do upvote if satisfied!**

Conduct the stated hypothesis test for μ 1− μ 2. μ 1−
μ 2. Assume that the samples are independent and randomly selected
from normal populations with equal population
variances ( σ 12= σ 22)( σ 12= σ 22).
H0 : μ 1− μ 2=0H0 : μ 1− μ 2=0
H1 : μ 1− μ 2 < 0H1 : μ 1− μ 2 <
0
α =0.025 α =0.025
n1=27n1=27
x̄ 1=8.76 x̄ 1=8.76
s1=1.26s1=1.26
n2=25n2=25
x̄ 2=9.44 x̄ 2=9.44
s2=1.29
a. Calculate the test...

1. A sampling distribution of the mean has a
mean μ X̄ =45 μ X̄ =45 and a
standard error σ X̄ =7 σ X̄ =7
based on a random sample of n=15.n=15.
a. What is the population mean?
b. What is the population standard
deviation?
Round to two decimal places if necessary
2. If it is appropriate to do so, use the normal approximation
to the p^ p^ -distribution to calculate the
indicated probability:
Standard Normal Distribution Table
n=80,p=0.715n=80,p=0.715
P( p̂ > 0.75)P( p̂ > 0.75) =
Enter 0...

2.) Assume that you have a sample of n1 = 8, with the sample
mean X overbar 1= 42, and a sample standard deviation of S1 = 4,
and you have an independent sample of n2=15 from another population
with a sample mean of X overbear 2 = 34 and a sample standard
deviation of S2 = 5.
What assumptions about the two populations are necessary in
order to perform the pooled-variance t test for the hypothesis H0:
μ1=μ2 against...

he restaurant manager is testing the bartender's ability to pour
45 mL of spirits correctly into a mixed drink. The manager has the
bartender pour water into 12 shot glasses to test their ability to
pour the correct amount of spirits:
48
45
44
43
46
47
42
46
47
45
47
49
Note: The data appears to be approximately normally
distributed.
Test the bartender's ability to pour 45 mL at the 1% level of
significance.
T-Distribution Table
a. Calculate...

Conduct the stated hypothesis test for μ 1− μ 2. μ 1−
μ 2. Assume that the samples are independent and randomly selected
from normal populations.
H0 : μ 1− μ 2=0H0 : μ 1− μ 2=0
H1 : μ 1− μ 2 ≠ 0H1 : μ 1− μ 2 ≠ 0
α =0.02 α =0.02
n1=37n1=37
x̄ 1=2,263 x̄ 1=2,263
σ 1=150 σ 1=150
n2=33n2=33
x̄ 2=2,309 x̄ 2=2,309
σ 2=177.3 σ 2=177.3
Standard Normal Distribution Table
a. Calculate the test statistic.
z=z=
Round...

A random sample of n1 = 52 men and a random sample of
n2 = 48 women were chosen to wear a pedometer for a
day.
The men’s pedometers reported that they took an average of 8,342
steps per day, with a standard deviation of
s1 = 371 steps.
The women’s pedometers reported that they took an average of
8,539 steps per day, with a standard deviation of s2 =
214 steps.
We want to test whether men and women...

To test H0: σ=2.2 versus H1: σ>2.2, a random sample of size
n=15 is obtained from a population that is known to be normally
distributed. Complete parts (a) through (d).
(a) If the sample standard deviation is determined to be s=2.3,
compute the test statistic.
χ^2_0=____
(Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the
α=0.01 level of significance, determine the critical value.
χ^2_0.01=____
(Round to three decimal places as needed.)...

1) The sample mean and standard deviation from a random sample
of 22 observations from a normal population were computed as x¯=40
and s = 13. Calculate the t statistic of the test required to
determine whether there is enough evidence to infer at the 7%
significance level that the population mean is greater than 37.
Test Statistic=
2) The contents of 33 cans of Coke have a mean of x¯=12.15 and a
standard deviation of s=0.13. Find the value...

A random sample of n1 = 10 winter days in
Denver gave a sample mean pollution index x1 =
43. Previous studies show that σ1 = 21. For
Englewood (a suburb of Denver), a random sample of
n2 = 12 winter days gave a sample mean
pollution index of x2 = 36. Previous studies
show that σ2 = 13. Assume the pollution index
is normally distributed in both Englewood and Denver.
(a) Do these data indicate that the mean population...

Given two independent random samples with the following
results:
n1= 350 n2= 475
pˆ1=0.55 pˆ2=0.68
Can it be concluded that the proportion found in Population 2
exceeds the proportion found in Population 1? Use a significance
level of α=0.05 for the test.
State the null and alternative hypotheses for the test
Find the values of the two sample proportions, pˆ1 and pˆ2.
Round to 3 decimal places
Compute the weighted estimate of p, p‾. Round to 3 decimal
places
Compute...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 12 minutes ago

asked 18 minutes ago

asked 31 minutes ago

asked 34 minutes ago

asked 36 minutes ago

asked 40 minutes ago

asked 46 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago