Test the hypothesis using the P-value approach.

Falak Kinney 2021-05-27 Answered

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
H0: P=0.52 versus H1:p<0.52
N=150,X=72,α=0.1
Is NP0(1P0) greater than or equal to 10?
Use technology to find the P-Value.

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Expert Answer

pattererX
Answered 2021-05-28 Author has 95 answers

Null hypothesis, H0:P=0.52
Alternative hypothesis, H1:P<0.52
Under H0, the population proportion is P0=0.52
Now consider,
NP0(1P0)=150×0.48×(10.48)
=37.44
>10
Since NP0(1P0)  is greater than or equals to 10, use normal approximation to test the true proportion.
Given information:
Number of trials, N=150
Number of sucesses in 150 cases, X=72
Sample proportion,
p=XN
=72150
=0.48
Compute test statistic.
z=pP0P0(1P0)N
=0.480.52(0.52)(10.52)N
=0.98058
=0.98
Alternative hypothesis has symbol "<", so the test is based on left-tailed.
Using Excel function "=NORMSTD(z)"
Pvalue=P(Zz)
=P(Z0.98)
=NORMSDIST(0.98)
=0.1635
When testing the hypothesis H0:P=0.52 versus H1:P<0.52, using the sample information N=150 and X=72, the P-value of test is 0.1635

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