Question

Mr. Jones wanted to check if there was an observable impact of a particular worksheet on his students’ test scores for Chapter 1. His idea was to test if there was a significant variation in the average test score of the class that used the worksheet in comparison to the class that did not. In the class before lunch, he used the worksheet but not the one after lunch. He has 23 students in each class. Their test scores are below:

Before Lunch		After Lunch
86	79	23	67
59	45	74	46
98	67	38	90
81	80	14	79
32	72	38	63
35	84	51	38
31	60	18	56
57	20	44	70
68	43	27	33
24	16	16	14
31	58	24	30
82		17

1. Which test are you using?
2. What are your H0 (null hypothesis) and Ha (alternative hypothesis)?
3. Calculate your statistic.
4. What decision does this inform you to make and why? (You may use the critical value in the chart or the calculated p-value, but you must indicate what you are doing.)
5. Write a one to two sentence conclusion that correctly responds to the question.

Answer 1

a)

Since

1) samples are paired and 2) sample size is not large

non- pamametric sign test is prefered.

b)

The hypotheses are given below.

(null hypothesis) H₀: The median difference is zero

versus

(alternative hypothesis) H₁: The median difference is not zero.

c) Counting the number of positives and negatives

The test statistic is the number of negative signs.(number of positive signs, whichever is smaller.)

• 17 positives.
• 6 negatives.

d)

We have a critical value of 6 from table and p-value is 0.037

Since the P-value is less than 0.05(> 0.037). Therefore, we can reject the null hypothesis. There is sufficient evidence, at the 0.05 level there is a significant median difference.

e)

There is sufficient evidence of significant variation in the average test score of the class that used the worksheet in comparison to the class that did not.(Mr. Jones idea to test if there was significant variation was right )