Question

Consider the following hypotheses and the sample data in the accompanying table. Answer the following questions using aα ​= 0.01.

8 9 10 8 7 8 10 9 11 6 5 9 9 10 10

H0​: μ=10

H1​: μ≠10

a. What conclusion should be​ drawn?

b. Use technology to determine the​ p-value for this test.

a. Determine the critical​ value(s).

The critical​ value(s) is(are) . ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Determine the test​ statistic, t-x

t-x=

What conclusion should be​ drawn? Choose the correct answer below.

A. Reject the null hypothesis. The data do not provide do not provide sufficient evidence to conclude that the mean differs from μ=10

B. Do not reject Do not reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ =10.

C. Do not reject Do not reject the null hypothesis. The data do not provide do not provide sufficient evidence to conclude that the mean differs from μ=10

D. Reject Reject the null hypothesis. The data provide provide sufficient evidence to conclude that the mean differs from μ = 10

b. Use technology to determine the​ p-value for this test. What is the​ p-value

​p-value equals = ​(Round to three decimal places as​ needed.) .

Answer 1

Solution:

x	x2
8	64
9	81
10	100
8	64
7	49
8	64
10	100
9	81
11	121
6	36
5	25
9	81
9	81
10	100
10	100
x=129	x2=1147

Mean ˉx =xn

=8+9+10+8+7+8+10+9+11+6+5+9+9+10+10 /15

=129 /15

=8.6

The sample standard is S

  S =  ( x² ) - (( x)² / n ) n -1

=1147-(129)²15 /14

=1147-1109.4/14

=37.6/14

=2.6857

=1.6388

= 10

=8.6

s = 1.64

n = 15

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 10

H_a :     10

Test statistic = t

= ( - ) / s / n

= (8.6- 10) / 1.64/ 15

= −3.306

Test statistic = t = −3.306

P-value =0.005

= 0.01

0.005 < 0.01

. Reject Reject the null hypothesis. The data provide provide sufficient evidence to conclude that the mean differs from μ = 10