Question

The average IQ is 100. Below is a sample of 8 left-handed individuals who have been given an IQ test. Test the hypothesis that left-handed individuals have different IQs than the average American. Use an alpha level of .01.

IQ

120

90

110

100

80

90

100

90

1. (2 pts) What is the appropriate test?
2. (1 pt) State the null hypothesis:
3. (1 pt) State the alternative hypothesis:
4. (2 pts) Find the critical value:
5. (2 pts) Calculate the obtained statistic:
6. (1 pts) Make a decision:
7. (1 pt) What does your decision mean?
8. (2 pts) Compute this test using SPSS and paste the relevant output below, confirming the same result as you have obtained by-hand above.

Answer 1

Answer)

A)

As the population s.d is unknown here

Appropriate test is one sample t test

B)

Null hypothesis Ho : u = 100

C)

Alternate hypothesis Ha : u not equal to 100

D)

N = 8

Degrees of freedom is = n-1 = 7

For 7 degrees of freedom and 0.01 alpha

Critical values from t table is = -3.499 and 3.499

E)

Test statistics = (sample mean - claimed mean)/(s.d/√n)

Sample mean = 97.5

S.d = 12.8174

Claimed mean = 100

N = 8

After substitution

Test statistics = -0.552

F)

Rejection region is

Reject null hypothesis Ho

If test statistics is less than -3.499 or greater than 3.499

As -0.552 is not less than -3.499

We fail to reject the null hypothesis Ho

G)

We do not have enough evidence to conclude that mean is different than 100