Question

**Age and Vocabulary** Researchers claim that there
is significant *positive linear correlation* between
population age and vocabulary based on a sample of nine children
with correlation coefficient r = 0.841. Test this claim at the 95%
confidence level. Select one for each blank.

(a) Hypotheses:

H0: [r, rho, x, mu] [=, >=, <=, >, >] 0

Ha: [r, rho, x, mu] [=, >=, <=, >, <] 0

(b) Type of test: [Two sided, Right sided, Left sided]

(c) Choice of distribution: [normal, t-distribution, chi-squared distribution]

(d) Critical value: [1.645, 1.860, 1.895, 1.96, 2.306, 2.365]

(e) Test statistic value: [0, 0.05, 0.841, 0.95, 1] .Standardized test statistic value: [0.841, 1.96, 2.435, 4.113, 6.289]

(f) Reject or fail to reject: Since the standardized test value is [equal to, greater than, less than] the critical value, we [reject, fail to reject, prove, support] the null.

(g) Interpret: There is enough evidence at the 5% significance level to [support, reject] the claim that there is a significant positive linear correlation between age and vocabulary.

Answer #1

r=0.841

n=9

95% confidence level

a)

H0: rho= 0

Ha: rho>0

b)

Type of test: right sided one tail test

c)

t-distribution

d)*d**f*=*n*−2=9−2=7

alpha=0.05

right tail

Critical value:2.365

e)

.Standardized test statistic value-

f)

Reject null hypothesis

Since the standardized test value is **greater
than** the critical value, we reject the null.

g)

Interpret: There is enough evidence at the 5% significance level
to **support** the claim that there is a significant
positive linear correlation between age and vocabulary

Use the given sample statistics to test the claim about the
difference between two population means
mu 1μ1 and mu μ2 at the given level of significance
alphaα=0.01.
Claim: mu 1μ1greater than>mu 2μ2,
Statistics: x overbar 1=5.2, s1=0.30, n1=48 and x overbar
2=5.6, s2=0.7 n2=37
Choose the correct null and alternative hypotheses below.
A. Upper H 0: mu 1greater thanmu 2 (Claim) Upper H Subscript
a: mu 1less than or equalsmu 2
B. Upper H 0: mu 1not equalsmu 2...

The ages (in years) of eight children and the number of words in
their vocabulary are noted in the table below. Find the correlation
( r ) and then test to see if there is enough evidence to conclude
that there is a significant linear correlation between the
data.
Vocabulary
Age
Size
x
y
1
3
2
440
3
1200
3
1100
4
1500
5
2100
5
2000
6
2600
What is r?
Ho:?
Ha:?
Level of Significance (alpha):?
Number...

Test the correlation between age and amount of time spent per
day in hours listening to music. Use α = 0.05.
X(Age)
Y (Hours per day )
40
1
15
5
18
5
22
3
30
2
State the claim:
H 0 ρ = 0 C l a i m
H 1 ρ ≠ 0
Critical Values =+/- use table I
Compute Correlation Coefficient: r = (round to 3
place values)
Make a decision to Reject or...

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 linear correlation between the
age of a driver and the number of driver deaths. The following
table represents the age of a driver and the number of driver
deaths per 100,000. Use a significance level of 0.05 and round all
values to 4 decimal places.
Driver Age
Number of Driver Deaths per 100,000
28
22
26
30
56
30
52
23
77
33
36
22
78
22
38
26
77
36
62
30
Ho:...

You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.01. You have the
following bivariate data set.
x
y
8.8
46.6
30.2
68.7
42.7
61.8
30.8
83.1
27.3
45.1
26.9
46.1
32
110.2
9.2
25.9
18.4
102.7
42
51.8
10.4
86.1
46.3
41.1
12.7
42.9
19.6
27.3
22.9
59.5
26.9
59.7
2.4
46.8
What is the critical value for this hypothesis test?
rc.v. =
What is the correlation coefficient for...

Test the claim about the population mean,μ, at the given level
of significance using the given sample statistics
Claim: μ not equal 7000; alpha=0.09; sigma (SD) =374.
Samplestatistics: x =7300, n=34
1. identify the null and alternative hypotheses
2. what is the standardized test statistic
3. Determine the critical value (round to two decimal places as
needed)
4. Determine the outcome and conclusion of the test (choose from
choices below)
a. Fail to reject H0 - not enough evidence to...

You wish to determine if there is a positive linear correlation
between the two variables at a significance level of α=0.01α=0.01.
You have the following bivariate data set.
x
y
54.5
82.1
45.8
20.9
46.4
22.7
44.8
-5.5
38.8
-5.4
35.4
83.5
44.3
96.3
25
-45.1
47.8
29.8
48.8
6
49.9
40.6
50.2
62.7
42.1
20.4
32.3
-40.2
45.1
30.5
49.3
3.4
29.4
27.7
44
2.3
39.2
18.2
37.5
1
44.1
27.1
50.6
-41.3
42.9
90.5
39.2
4.5
40.2
-60.7...

Some researchers claim that herbal supplements improve human
memory. To test this claim, a researcher selects a sample of n = 25
college students. Each student is given herbal supplements daily
for 6 weeks and then all the participants are given a standardized
memory test. For the population, scores on the tests are normally
distributed with µ = 70 and σ= 15. The sample of n = 25 students
had a mean score of M = 75. Can we conclude...

Runs Test/G:
Consider the following sequence:
DDD EE DDD EE DD E DD EEE DD E DDDD EEEEE DD
With a 0.05 significance level, we wish to test the claim that
the above sequence was produced in a random manner. Answer each of
the following questions
(a) The null hypothesis H0 is given by
A. Median=0
B. ρ=0
C. The data are in a random order
D. The data are in an order that is not
random
E. β=0
F....

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 2 minutes ago

asked 3 minutes ago

asked 4 minutes ago

asked 8 minutes ago

asked 25 minutes ago

asked 25 minutes ago

asked 33 minutes ago

asked 33 minutes ago

asked 44 minutes ago

asked 50 minutes ago

asked 56 minutes ago