Question

Listed below are ten randomly selected IQ scores of statistics students:

111   115   118 100   106   108   110   105   113   109

Using methods for hypothesis testing, you can confirm that these data have the following sample statistics: n = 10,   

109.5, s = 5.2

Using a 0.05 significance level, test the claim that statistics students have a mean IQ score greater than 100, which is the mean IQ score of the general population.

Answer 1

Here we have given that,

Xi: IQ scores

Xi
111
115
118
100
106
108
110
105
113
109

n= Number of observation =10

= sample mean =109.5

S= sample standard deviation =5.2

= population mean IQ score = 100

Claim: To check whether the statistics students have a mean IQ score greater than 100

The Hypothesis is as follows

v/s

this is right (one) tailed test as our interest is in

We have given that,Now, we can find the test statistic

t-statistics=

=

=5.78

we get,

the Test statistic is 5.78

Now we find the P-value

= level of significance=0.05

This is right one tailed test

Degrees of freedom=n-1=10-1=9

Now, we can find the P-value

P-value =0.0001 Using EXCEL= TDIST(| t-statistics |= 5.78 , D.F= 9, tail=1)

we get the P-value is 0.0001

Decision:

P-value < 0.05 ()

That is we reject Ho (Null Hypothesis)

Conclusion

There is the sufficient evidence that the statistics students have a mean IQ score greater than 100