SOLUTION: Consider the following hypotheses: H0: p ≥ 0.47 HA: p < 0.47 Compute the p-value based on the following sample information. p-value a. x

Question 1163221: Consider the following hypotheses:
H0: p ≥ 0.47
HA: p < 0.47
Compute the p-value based on the following sample information.
p-value
a. x = 46 ; n = 118 _________________
b. x = 112 ; n = 311 _________________
c. p¯= 0.38 ; n = 53 _________________
d. p¯= 0.38 ; n = 430 _________________
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
d. z=(p hat-p)/sqrt (p*(1-p)/n)
=-0.09/sqrt(.47*.53/430); sqrt term is 0.0241
z=-3.74
p<0.0001 (it is 0.000079)-once the p-value is less than 0.0001, it usually is immaterial what it is exactly.
The calculator will give a slightly different result, because there is not an integer value with a denominator of 430 that gives a probability of 0.38
b. Here p hat is 0.3601
z=0.3601-0.47 divided by sqrt (p(1-p)/n) and that is sqrt(0.47*0.53/311). The sqrt term is 0.0283
z=-0.1099/0.0283 or -3.883
p-value again <0.0001 and 0.00005
Others are done the same way.

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