Question

Consider a sample of 52 football games, where 32 of them were won by the home team. Use a 0.01 significance level to test the claim that the probability that the home team wins is greater than one-half. Identify the null and alternative hypotheses for this test.

Answer #1

Given:

Number of favourable cases, X = 32

Sample size, n = 52

Significance level, = 0.01

Sample proportion, = X/n = 32/52 = 0.6154

Hypothesis test:

The null and alternative hypothesis is

H0 : p 0.5 (p = 0.5 also true)

Ha : p > 0.5 (This is a right tailed test)

Test statistics is

z = - p/√p(1-p/n

= 0.6154-0.5/√0.5(1-0.5)/52

= 1.6642

Test statistics is z = 1.66

**P-value for right tailed test:**

P-value = P(Z>1.66) = 0.0485...(from z table)

Since P-value is greater than significance level 0.01, we fail to reject null hypothesis.

Decision: Fail to reject H0.

Conclusion : At 0.01 significance level, there is not sufficient evidence to conclude that the probability that the home team wins is greater than one-half.

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48
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26
of them were won by the home team. Use a
0.01
significance level to test the claim that the probability that
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were won by the home team. Use a 0.01
significance level to test the claim that the probability that
the home team wins is greater than one-half.
____________________________________________________
Identify the null and alternative hypotheses for this test.
Choose the correct answer below.
A.
H0:
p=0.5
H1:
p>0.5
B.
H0:
p>0.5
H1:
p=0.5
C.
H0:
p=0.5
H1:
p≠0.5
D.
H0:
p=0.5
H1:
p<
___________________________________
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