Question

# Independent random samples of n1 = 170 and n2 = 170 observations were randomly selected from...

Independent random samples of

n1 = 170

and

n2 = 170

observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 96 successes, and sample 2 had 103 successes.

You wish to perform a hypothesis test to determine if there is a difference in the sample proportions

p1

and

p2.

(a)

State the null and alternative hypotheses.

H0: (p1p2) < 0 versus Ha: (p1p2) > 0

H0: (p1p2) = 0 versus Ha: (p1p2) ≠ 0

H0: (p1p2) ≠ 0 versus Ha: (p1p2) = 0

H0: (p1p2) = 0 versus Ha: (p1p2) > 0

H0: (p1p2) = 0 versus Ha: (p1p2) < 0

(b)

Find the test statistic and rejection region, using the α = 0.10 level of significance. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statisticz=rejection regionz>z<

(c)

H0 is rejected. There is insufficient evidence to indicate that p1 is different from p2.H0 is rejected. There is sufficient evidence to indicate that p1 is different from p2.    H0 is not rejected. There is sufficient evidence to indicate that p1 is different from p2.H0 is not rejected. There is insufficient evidence to indicate that p1 is different from p2.

Independent random samples of

n1 = 170

and

n2 = 170

observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 96 successes, and sample 2 had 103 successes.

You wish to perform a hypothesis test to determine if there is a difference in the sample proportions

p1

and

p2.

(a)

State the null and alternative hypotheses.

H0: (p1p2) < 0 versus Ha: (p1p2) > 0

H0: (p1p2) = 0 versus Ha: (p1p2) ≠ 0

H0: (p1p2) ≠ 0 versus Ha: (p1p2) = 0

H0: (p1p2) = 0 versus Ha: (p1p2) > 0

H0: (p1p2) = 0 versus Ha: (p1p2) < 0

(b)

Find the test statistic and rejection region, using the α = 0.10 level of significance. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statisticz=rejection regionz>z<

(c)

H0 is rejected. There is insufficient evidence to indicate that p1 is different from p2.H0 is rejected. There is sufficient evidence to indicate that p1 is different from p2.    H0 is not rejected. There is sufficient evidence to indicate that p1 is different from p2.H0 is not rejected. There is insufficient evidence to indicate that p1 is different from p2.

a)

H0: (p1 − p2) = 0 versus Ha: (p1 − p2) ≠ 0

b)

p1cap = X1/N1 = 96/170 = 0.5647
p1cap = X2/N2 = 103/170 = 0.6059
pcap = (X1 + X2)/(N1 + N2) = (96+103)/(170+170) = 0.5853

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5647-0.6059)/sqrt(0.5853*(1-0.5853)*(1/170 + 1/170))
z = -0.77

c)

H0 is not rejected.There is insufficient evidence to indicate that p1 is different from p2.

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