Question

You believe the rate of students who fail the SOL is lower for school A than school B. A random sample of 500 students from school A showed that 5.8% failed. A random sample of 400 students from school B revealed that 7.5% failed.

A: Verify the assumptions.

B:State the hypotheses

C:What is the test statistic?

D:Test this hypothesis at the significance level .02

E:What is your conclusion?

Answer 1

a)
• The two samples must be independently drawn and reasonably random or subjects were
randomly assigned to two groups.
• The sample sizes must be large enough so that: 1 1 n pˆ , 1 1 n p (1 ) − ˆ , 2 2 n pˆ , 2 2 n p (1 ) − ˆ are all five
or more. (the number of successes and the number of failures must be at least 5) for the
confidence interval.
The sample size must be large enough so that: 1 ˆ c n p , 1(1 ) ˆ c n p − , 2 ˆ c n p , 2 (1 ) ˆ c n p − are all five or
more. (the number of successes and the number of failures must be at least 5) for the
significance test.

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

c)

p1cap = X1/N1 = 29/500 = 0.058
p1cap = X2/N2 = 30/400 = 0.075
pcap = (X1 + X2)/(N1 + N2) = (29+30)/(500+400) = 0.0656

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.058-0.075)/sqrt(0.0656*(1-0.0656)*(1/500 + 1/400))
z = -1.02

d)

P-value Approach
P-value = 0.1539

e)

As P-value >= 0.05, fail to reject null hypothesis.