Question

1. A particular resource class must perform at a level consistent with the rest of the school to avoid being discontinued. On the first quarter statewide test, the mean score of the school was 84. The 14 students in the resource class had a 76.17 mean test score and a 17.52 standard deviation. The district informs the principal that the class should be discontinued because the average is below that of the rest of school. Is this reasonable or does the principal have evidence to support an argument against this decision?

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)

t test because n<30

b)

Null Hypothesis: H0 :μ = 84
Alternative Hypothesis: Ha :μ < 84

c)

Test statistic,
t = (x bar - u)/(s/sqrt(n))
t = (76.17 - 84)/(17.52/sqrt(14))
t = -1.67221

d)

Using P-value Approach
P-value = 0.059182

e)

As P-value(0.06) >= 0.05

Since p value is greater, We fail to reject the null hypothesis.

There is not sufficient evidence to conclude that class should be discontinued because the average is below that of the rest of the school.

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