Find the value of the test statistic

Question

I would really appreciate the help guys. Thanks again !

 

1)the claim is that the proportion of peas with yellow pods is equal to 0.25 the sample statistics from one experiment include 560 peas with 161 of them having yellow pods. Find the value of the test statistic

 

2)The Claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.30, and the sample statistics include n=1427 subjects with 457 saying that they smoked a cigarette in the past week. Find the value of the test statistic. 

Answer 1

 

 P :  sample proportion

 p0 : hypothesis proportion

 n : is the sample size

 

 

Then denominator D = sqrt ( p0 ( 1 - p0) / n)

 

The test stat is z= (p - p0)/ D  

 

 

(1)   n = 560 so P = 161/560 = 0.2875

 

       D = sqrt(  0.25 * (1 - 0.25) / 560 ) = sqrt ( 0.25 * 0.75 / 560 ) = 0.0183 approximately

      

       The test stat z = ( 0.2875 - 0.25 ) / 0.0183 = 2.049

 

        Per the normal bell curve, reject the null hypothesis; statistical evidence suggests the population

        proportion is not 0.25 ( potentially greater than)

 

(2)  N=1427   P = 457/1427 = 0.3202

 

      D = sqrt ( 0.3 * (1 - 0.3)/1427) = sqrt ( 0.3 * 0.7 / 1427) = 0.01213103 approximately

 

      Test test stat is ( 0.3202 - 0.3) / 0.01213103 = 1.66515127

 

     This is less than critical values for most confidence levels ( 95% certainty requires 1.96)

      The statistical evidence supports the claim; accepts null hypothesis. Notice the sample size is 

     much larger than the previous