Question

A sample of freshmen takes a reading comprehension test and their scores are summarized below. If the mean for the general population on this test is m = 12, can you conclude that this sample is significantly different from the population. Test with a = .05.
Sample Scores: 16, 8, 8, 6, 9, 11, 13, 9, 10

A. Find M=

B.Find SS=

C.Find standard error =

D.Find t =

E. Choose one:

Reject H₀ =1

Fail to Reject H₀ =2

Answer 1

Solution:

We are given a data of sample size n = 9

16, 8, 8, 6, 9, 11, 13, 9, 10

Using this, first we find sample mean() and sample standard deviation(s).

=   

= ( 16 + 8.......+ 10 ) / 9

= 10

Now ,

s=   

Using given data, find Xi - for each term.Take square for each.Then we can easily find s.

s = 3

The standard error of mean = / n = 3 / 9 = 1

The null and alternative hypothesis are,

H0   ; 12 ........ Null hypothesis

Ha ;   12 ......... Alternative hypothesis

Given, n = 9 , x = 10 , s = 3

The test statistic is,

t = Xˉ−μ0​​ / / n

= 10 - 12 / 3 / 9

= -2.00

Then, n = 9 , df = n - 1 = 8

sign in Ha === two tailed test

Using , t = -2.00 , df = 8 , two tailed test

p - value = 0.0805

Since,

p - value = 0.0805 > alpha = 0.05

Fail to Reject the null hypothesis.