Given that, the null and alternative hypotheses are,
H0 : p ≥ 0.48
HA : p < 0.48
This hypothesis test is a left-tailed test.
a) x = 47 and n = 127
=> sample proportion = 47/127 = 0.3701
Test statistic is,
=> Test statistic = Z = -2.48
p-value = P(Z < -2.48) = 1 - P(Z < 2.48) = 1 - 0.9934 = 0.0066
=> p-value = 0.0066
b) x = 124 and n = 327
=> sample proportion = 124/327 = 0.3792
Test statistic is,
=> Test statistic = Z = -3.65
p-value = P(Z < -3.65) = 1 - P(Z < 3.65) = 1 - 0.9999 = 0.0001
=> p-value = 0.0001
c) n = 54
=> sample proportion = 0.41
Test statistic is,
=> Test statistic = Z = -1.03
p-value = P(Z < -1.03) = 1 - P(Z < 1.03) = 1 - 0.8485 = 0.1515
=> p-value = 0.1515
d) n = 444
=> sample proportion = 0.41
Test statistic is,
=> Test statistic = Z = -2.95
p-value = P(Z < -2.95) = 1 - P(Z < 2.95) = 1 - 0.9984 = 0.0016
=> p-value = 0.0016
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