Question

the following 13th of the same month. Use a 0.05 significance level to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected.

Friday the 6th: 9 6 11 11 3 5

Friday the 13th: 13 12 13 10 5 11

What are the hypotheses for this test?

Let μd be the (mean of the difference,differences between the mean)

n the numbers of hospital admissions resulting from motor vehicle crashes for the population of all pairs of data.

H0:μd (= > < ≤ ≥ ≠) 0

H1: μd (< > = ≠ ≤ ≥) 0

Find the value of the test statistic.

t=

(Round to three decimal places as needed.)

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

(Round to three decimal places as needed.)

A.The critical value is

t=.

B.The critical values are

t=± ?.

State the result of the test. Choose the correct answer below.

A.There is not sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected.

B.There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions do not appear to be affected.

C.There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected.

D.There is not sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions do not appear to be affected.

Answer #1

Let us denote

d = Friday the 6th - Friday the 13th

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H_{0} follows a t distribution with n-1 df.

We reject H_{0} at 0.05 level of significance if

Now,

The value of the test statistic

and critical value

Since
, so we reject H_{0} at 0.05 level of significance.

We can conclude that :

C.There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected.

Researchers collected data on the numbers of hospital admissions
resulting from motor vehicle crashes, and results are given below
for Fridays on the 6th of a month and Fridays on the following 13th
of the same month. Use a 0.05 significance level to test the claim
that when the 13th day of a month falls on a Friday, the numbers
of hospital admissions from motor vehicle crashes are not
affected
Friday the 6th:
Friday the 13th:
9
14
7
14...

Researchers collected data on the numbers of hospital admissions
resulting from motor vehicle crashes, and results are given below
for Fridays on the 6th of a month and Fridays on the following 13th
of the same month. Use a 0.05 significance level to test the claim
that when the 13th day of a month falls on a Friday, the numbers
of hospital admissions from motor vehicle crashes are not
affected.
Friday the 6th: Friday the 13th:
10 14
6 12...

Researchers collected data on the numbers of hospital admissions
resulting from motor vehicle crashes, and results are given below
for Fridays on the 6th of a month and Fridays on the following 13th
of the same month. Use a 0.05 significance level to test the claim
that when the 13th day of a month falls on a Friday, the numbers
of hospital admissions from motor vehicle crashes are not
affected.
Friday the 6th: Friday the 13th:
10 14
5 11...

Data on the numbers of hospital admissions resulting from motor
vehicle crashes are given below for Fridays on the 6th of a month
and Fridays on the following 13th of the same month. Assume that
the paired sample data is a simple random sample and that the
differences have a distribution that is approximately normal.
Construct a 95% confidence interval estimate of the mean of the
population of differences between hospital admissions. Use the
confidence interval to test the claim...

Data on the numbers of hospital admissions resulting from motor
vehicle crashes are given below for Fridays on the 6th of a month
and Fridays on the following 13th of the same month. Assume that
the paired sample data is a simple random sample and that the
differences have a distribution that is approximately normal.
Construct a 95% confidence interval estimate of the mean of the
population of differences between hospital admissions. Use the
confidence interval to test the claim...

Researchers collected data on the numbers of hospital admissions
resulting from motor vehicle crashes and results are given below
for Fridays on the 6th of a month and Fridays on the following 13th
of the same month. Construct a 95% confidence interval estimate of
the mean of the population of differences between hospital
admissions on days that are Friday the 6th of a month and days that
are Friday the 13th of a month. Use the confidence interval to test...

Data on the numbers of hospital admissions resulting from motor
vehicle crashes are given below for Fridays on the 6th of a month
and Fridays on the following 13th of the same month. Assume that
the paired sample data is a simple random sample and that the
differences have a distribution that is approximately normal.
Construct a95% confidence interval estimate of the mean of the
population of differences between hospital admissions. Use the
confidence interval to test the claim that...

Data on the numbers of hospital admissions resulting from motor
vehicle crashes are given below for Fridays on the 6th of a month
and Fridays on the following 13th of the same month. Assume that
the paired sample data is a simple random sample and that the
differences have a distribution that is approximately normal.
Construct a 95% confidence interval estimate of the mean of the
population of differences between hospital admissions. Use the
confidence interval to test the claim...

Data on the numbers of hospital admissions resulting from motor
vehicle crashes are given below for Fridays on the 6th of a month
and Fridays on the following 13th of the same month. Assume that
the paired sample data is a simple random sample and that the
differences have a distribution that is approximately normal.
Construct a 95% confidence interval estimate of the mean of the
population of differences between hospital admissions. Use the
confidence interval to test the claim...

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