Question

A random sample of 10 observations was drawn from a large normally distributed population. The data is below.

21 26 27 21 19 28 25 25 20 20

Test to determine if we can infer at the 7% significance level that the population mean is not equal to 23, filling in the requested information below.

The p-value is =

Your decision for the hypothesis test:

A. Reject ?0.

B. Reject ?1.

C. Do Not Reject ?1.

D. Do Not Reject ?0.

Answer 1

Solution:

x	x2
21	441
26	676
27	729
21	441
19	361
28	784
25	625
25	625
20	400
20	400
---	---
∑x=232	∑x2=5482

The sample mean is

Mean = (x / n) )

=21+26+27+21+19+28+25+25+20+2010

=23210

=23.2

Mean =23.2

The sample standard is S

  S =( x2 ) - (( x)2 / n ) n -1

=5482-(232)2109

=5482-5382.49

=99.69

=11.0667

=3.3267

The sample standard =3.33

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 23

Ha :     23

Test statistic = t

= ( - ) / / n

= (23.2-23) / 3.33 / 10

= 0.19

Test statistic = t = 0.19

P-value =0.8536

= 0.01  

P-value >

0.8536 > 0.07

Do not reject the null hypothesis .

There is insufficient evidence to suggest that