Question

Test for evidence of a linear association using the sample correlation r=0.68 and the sample size n=10.

State the null and alternative hypotheses.

Find the test statistic.

Round your answer to two decimal places.

t= Enter your answer; t

Find the *p*-value.

Round your answer to three decimal places.

The *p*-value is Enter your answer; p-value .

What is the conclusion, using a 5% significance level?

Choose the answer from the menu; What is the conclusion, using a 5%
significance level?
Do not rejectReject H0.

Is the correlation significant?

Choose the answer from the menu; Is the correlation
significant?
YesNo

Answer #1

State the null and alternative hypotheses.

Null hypothesis: H_{0}: The correlation coefficient is
not statistically significant.

Alternative hypothesis: H_{a}: The correlation
coefficient is statistically significant.

The test statistic value is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

t = 0.68*sqrt(10 - 2)/sqrt(1 - 0.68^2)

t = 2.623157

Test statistic = 2.62

df = n - 2 = 10 - 2 = 8

P-value = 0.030501

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

Is the correlation significant?

The correlation coefficient is statistically significant.

Test for a negative correlation using the sample correlation
r=-0.39 and the sample size n=18.
State the null and alternative hypotheses.
Find the test statistic.
Round your answer to two decimal places.
t=
Find the p-value.
Round your answer to three decimal places.
The p-value is .
What is the conclusion, using a 5% significance level?
...

Test for a positive correlation using the sample
correlationr=0.31and the sample sizen=30.
State the null and alternative hypotheses. Your answer should be
an expression composed of
symbols:=,≠,<,>,μ,μ1,μ2,p,p1,p2,0,1,ρ,p^,p^1,p^2,r.
H0: vs Ha
Find the test statistic.Round your answer to two decimal
places.
t=
Find the p-value.
Round your answer to three decimal places.
The p-value is
What is the conclusion, using a 5% significance level?
Choose the answer from the menu; What is the conclusion, using a 5%
significance level? ...

(a) Suppose n = 6 and the sample correlation
coefficient is r = 0.894. Is r significant at the
1% level of significance (based on a two-tailed test)? (Round your
answers to three decimal places.)
t
=
critical t
=
Conclusion:
Yes, the correlation coefficient ρ is significantly
different from 0 at the 0.01 level of significance.
No, the correlation coefficient ρ is not significantly
different from 0 at the 0.01 level of
significance.
(b) Suppose n = 10 and...

(a) Suppose n = 6 and the sample correlation coefficient is r =
0.908. Is r significant at the 1% level of significance (based on a
two-tailed test)? (Round your answers to three decimal places.) t =
critical t =
(b) Suppose n = 10 and the sample correlation coefficient is r =
0.908. Is r significant at the 1% level of significance (based on a
two-tailed test)? (Round your answers to three decimal places.) t =
critical t =

Use the normal distribution and the given sample results to
complete the test of the given hypotheses. Assume the results come
from a random sample and use a 5% significance level Test Ho: p =
0.5 vs Ha : p > 0.5 using the sample results p (hat) = 0.56 with
n = 25 Round your answer for the test statistic to two decimal
places, and your answer for the p value to three decimal places
test statistic = p...

2. Use the normal distribution and the given sample results to
complete the test of the given hypotheses. Assume the results come
from a random sample and use a 5% significance level. Test H0 :
p=0.25 vs Ha : p<0.25 using the sample results p^=0.15 with
n=100 Round your answer for the test statistic to two decimal
places, and your answer for the p-value to three decimal
places.
test statistic = _____________________
p-value = _____________________
Conclusion: ______________________ (Rejct or Do...

Activity 2: Hypothesis
test from start to finish
Is there evidence of a negative
correlation between systolic blood pressure and heart rate? In a
sample of 200 patients, we found a sample correlation of
-0.057.
State the hypotheses of interest.
H0:
rho=0 rho<0
What is the notation and value of the sample statistic?
r
Use StatKey to generate a randomization distribution for these
hypotheses. Use the data set ‘ICU Admissions’ available on
StatKey.
What is the
p-value?
0.211
Which two...

You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.10. You have the
following bivariate data set.
x
y
41.4
82.8
48.4
97.1
49.9
89.8
47
92.8
20.5
63.7
40.5
74.3
33
70.2
25.9
64.9
29.1
66.1
28.7
80.2
9.7
41.8
23.2
50.3
13.4
49
-5.2
25.4
23.8
56.2
22.5
53.3
30.9
67.4
7
39.6
18.7
46.4
10.5
25.8
What is the correlation coefficient for this data set?
r =...

Chapter 6, Section 5, Exercise 236 Use a t-distribution and the
given matched pair sample results to complete the test of the given
hypotheses. Assume the results come from random samples, and if the
sample sizes are small, assume the underlying distribution of the
differences is relatively normal. Assume that differences are
computed using d = x1-x2. Test H0 : ud=0 vs H0 : ud /= 0 using the
paired difference sample results x bar = 14.46, S= 13.0, n=25...

Given the linear correlation coefficient r and the sample size
n, determine the critical values of r and use your finding to
state whether or not the given r represents a significant linear
correlation. Use a significance level of 0.05. r=−0.816, n=5
A.Critical values: r=plus or minus±0.950, no significant
linear correlation
B.Critical values: r=plus or minus±0.878, significant linear
correlation
C.Critical values: r=0.950, significant linear correlation
D.Critical values: r=plus or minus±0.878, no significant
linear correlation

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