Question

The IQ scores for a small group of stats students are: 90, 91, 89.25, 87.5, 89, 90, 86, 92.8, 95, 88.3. Using the .01 significance level, how can I test the claim that stat students in general have IQ scores with a standard deviation that is 3  using the p- value method?

Answer 1

First we have to find sample standard deviation of the given sample using the excel function =STDEV.S( range of data set )

Therefore , S = 2.5908

Claim : Stat students in general have IQ scores with a standard deviation that is 3

: σ = 3 vs : σ ≠ 3

Test statistic :

   = =

= 6.7122

P-value :

We are given level of significance α = 0.01

Ha contain “≠” sign therefore this is two tail test.

df = n-1 = 9

We can use excel function =2*CHISQ.DIST(,df ,TRUE) to find P value for two tail test.

=2*CHISQ.DIST(6.7122,9 ,TRUE)

= 0.666

P value = 0.666

Decision:

As P value is greater than α = 0.01

We fail to reject H0,

Conclusion : We do not have significant evidence to reject the claim that Stat students in general have IQ scores with a standard deviation that is 3