A sample of 124 kissing couples were observed with 80 of the

A sample of 124 kissing couples were observed, with 80 of them leaning their heads to the right. Use these sample data to test whether or not the population proportion of kissing couples who lean their heads to the right differs from two-thirds.

a. Report the test statistic.

Round your answer to three decimal places.

b. Report the p-value.

Round your answer to four decimal places.

Solution

A)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.666666667
Ha:   p   =/=   0.666666667

As we see, the hypothesized po = 2/3 =   0.666666667      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.64516129      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.042333376      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -0.508000508   [ANSWER, TEST STATISTIC]

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b)  
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.611452987   [ANSWER, P VALUE]

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