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

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

pattererX · Accepted Answer

Null hypothesis, H0:P=0.52 Alternative hypothesis, H1:P&amp;lt;0.52 Under H0, the population proportion is P0=0.52 Now consider, NP0(1−P0)=150×0.48×(1−0.48) =37.44 &amp;gt;10 Since NP0(1−P0)  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=p−P0P0(1−P0)N =0.48−0.52(0.52)(1−0.52)N =−0.98058 =−0.98 Alternative hypothesis has symbol &quot;&amp;lt;&quot;, so the test is based on left-tailed. Using Excel function &quot;=NORMSTD(z)&quot; P−value=P(Z≤z) =P(Z≤−0.98) =NORMSDIST(−0.98) =0.1635 When testing the hypothesis H0:P=0.52 versus H1:P&amp;lt;0.52, using the sample information N=150 and X=72, the P-value of test is 0.1635

Test the hypothesis using the P-value approach.

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