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 H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.05 level of significance if

Now,

The value of the test statistic

and critical value

Since , so we reject H₀ 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.