Question

The number of hours 10 students spent studying for a test and their scores on that test are shown in the table. Is there enough evidence to conclude that there is a significant linear correlation between the data? Use alphaequals0.05.

Hours, x Test score, y

0 40

1 40

2 55

4 49

4 65

5 67

5 73

6 70

7 81

8 93

Setup the hypothesis for the test.

Upper H 0H0:

rhoρ

▼

less than or equals≤

less than<

equals=

greater than>

greater than or equals≥

not equals≠

0

Upper H Subscript aHa:

rhoρ

▼

less than or equals≤

less than<

equals=

greater than>

greater than or equals≥

not equals≠

0

Identify the critical value(s). Select the correct choice below and fill in any answer boxes within your choice.

(Round to three decimal places as needed.)

A.The critical value is

nothing.

B.The critical values are

minus−t 0t0equals=nothing

and

t 0t0equals=nothing.

Calculate the test statistic.

tequals=nothing

(Round to three decimal places as needed.)

What is your conclusion?

There

▼

is not

is

enough evidence at the

55%

level of significance to conclude that there

▼

is

is not

a significant linear correlation between hours spent studying and test score.

Answer #1

Let denotes the true correlation coefficient between hours and test score.

To test against

Here

sample correlation coefficient

and sample size

The test statistic can be written as

which under H_{0} follows a t distribution with n-2 df.

We reject H_{0} at 5% significance level if

Now,

The value of the test statistic =

and critical value

Since
, so we reject H_{0} at 5% significance level.

There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between hours spent studying and test score.

The number of hours10 students spent studying for a test and
their scores on that test are shown below. Is there enough
evidenceto conclude that there is a significant linear correlation
between the data. Use alpha=0.05
hours, x: 0 1 2 3 4 5 6 7 8 Test score, Y: 35 42 51 57 63 70 76
78 82 93 Setup the hypothesis for the test? identify the critical
value(s) calculate the test statistic? what is your conclusion?

Hours, x Test score, y
0 43
1 43
2 55
4 48
4 62
5 70
5 75
6 84
7 83
8 93
The number of hours
ten
students spent studying for a test and their scores on that test
are shown in the table. Is there enough evidence to conclude that
there is a significant linear correlation between the data?
Use
alphaαequals=0.01
Setup the hypothesis for the test.
Identify the critical value(s). Select the correct choice below...

The accompanying data have a sample correlation? coefficient,
rounded to three decimal? places, of negative 0.583. Perform a
hypothesis test with the data to determine if the population
correlation coefficient rho is less than zero using
alphaequals0.01.
x
8
5
3
2
5
y
5
9
9
7
6
What are the correct null and alternative? hypotheses?
A.
Upper H 0?: rho greater than or equals 0
Upper H 1?: rho less than 0
B.
Upper H 0?: rho equals...

Consider the hypothesis statement shown below using
alphaequals0.05 and the data to the right from two independent
samples.
Upper H 0 : mu 1 minus mu 2 greater than or equals 0
Upper H 1 : mu 1 minus mu 2 less than 0
?a) Calculate the appropriate test statistic and interpret the
result.
?b) Calculate the? p-value and interpret the result.
x overbar1
equals
121
x overbar2
equals
137
sigma1
equals
40
sigma2
equals
34
n1
equals
45
n2...

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Burger Stop is greater than the mean amount spent by a customer at
Fry World. The results for samples of customer transactions for the
two fast food restaurants are shown below. At
alphaαequals=0.05
can you support the magazine's claim? Assume the population
variances are equal. Assume the samples are random and
independent, and the populations are normally distributed. Complete
parts (a) through (e) below.
Burger Stop
Fry World...

The weights (in pounds) of
6
vehicles and the variability of their braking distances (in
feet) when stopping on a dry surface are shown in the table. Can
you conclude that there is a significant linear correlation between
vehicle weight and variability in braking distance on a dry
surface? Use
α=0.01.
Weight, x
5960
5370
6500
5100
5830
4800
Variability in braking distance, y
1.73
1.93
1.93
1.61
1.62
1.50
LOADING...
Click here to view a table of critical values...

The table below shows the number of hours per day 11 patients
suffered from headaches before and after 7 weeks of soft tissue
therapy. At alphaαequals=0.01,
is there enough evidence to conclude that soft tissue therapy
helps to reduce the length of time patients suffer from headaches?
Assume the samples are random and dependent, and the population is
normally distributed. Complete parts (a) through (f).
Patient Daily headache hours (before)
Daily headache hours (after)
1 3.1 2.4
2 1.8 2.2...

The dean of a university estimates that the mean number of
classroom hours per week for full-time faculty is
11.011.0.
As a member of the student council, you want to test this
claim. A random sample of the number of classroom hours for eight
full-time faculty for one week is shown in the table below. At
alphaαequals=0.100.10,
can you reject the dean's claim? Complete parts (a) through
(d) below. Assume the population is normally distributed.
10.810.8
9.49.4
12.712.7
6.16.1
4.94.9...

The table below gives the number of hours ten randomly selected
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this data, consider the equation of the regression line, yˆ=b0+b1x,
for predicting the test grade that a student will earn based on the
number of hours spent studying. Keep in mind, the correlation
coefficient may or may not be statistically significant for the
data given. Remember, in practice, it would not be appropriate to
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The table below gives the number of hours five randomly selected
students spent studying and their corresponding midterm exam
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practice, it would not be appropriate to use the regression line...

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