Question

Lary got a referral from a school to run an academic motivation program to 4th graders who got low grades in their last year. She wanted to check whether these students are below average for the intelligence level. The mean IQ of her students is 98, SD is 10, and she has 25 students. The average IQ is known as 100.

1. Indicate the null and research hypothesis.
2. What test do you do to test the null hypothesis above, among independent-sample t-test, paired-sample t-test, or one-sample t-test?
3. What is the t-statistics?
4. What is the d.f. for the test?
5. Do you reject the null hypothesis?
6. So, is the average IQ score of her class significantly different from 100?

Answer 1

Solution:

Indicate the null and research hypothesis.

Null hypothesis: H0: The average IQ of students is 100.

Alternative hypothesis: Ha: The average IQ of students is less than 100.

H0: µ = 100 versus Ha: µ < 100

This is a lower-tailed or left-tailed test.

What test do you do to test the null hypothesis above, among independent-sample t-test, paired-sample t-test, or one-sample t-test?

Answer: One-sample t-test

Here, we need to use one sample t test because we are not given the population standard deviation and sample size is small (n<30). Also, test is associated with one sample.

What is the t-statistics?

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 100

Xbar = 98

S = 10

n = 25

t = (98 – 100)/[10/sqrt(25)]

t = -1.00

Test statistic = -1.00

What is the d.f. for the test?

n = 25

df = n – 1 = 25 – 1 = 24

Do you reject the null hypothesis?

We assume α = 0.05

Critical value = -1.7109

(by using t-table or excel)

P-value = 0.1636

(by using t-table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the average IQ of students is less than 100.

So, the average IQ score of her class is not significantly different from 100.