You would like to determine if the population probability of success differs fro

Question

You would like to determine if the population probability of success differs from 0.75. You find 64 successes in 81 binomial trials. Implement the test at a 1% level of significance. Use Table 1.

a. Select the null and the alternative hypotheses.

b. Calculate the sample proportion. (Round your answer to 3 decimal places.)

c.

Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)

What is the conclusion?

b. Calculate the sample proportion. (Round your answer to 3 decimal places.)

c.

Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)

What is the conclusion?

Explanation / Answer

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.75
Ha:   p   =/=   0.75 [ANSWER]

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b)

As we see, the hypothesized po =   0.75      

Getting the point estimate of p, p^,          
          
p^ = x / n = 64/81 =   0.790123457   [ANSWER]

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c)  
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.048112522      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    0.833950389   [ANSWER, TEST STATISTIC]

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d)  
          
As this is a    2   tailed test, then, getting the p value,  
          
p = 0.4066 [ANSWER]

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e)

As P > 0.01, we fail to reject Ho.

There is no significant evidence that the population probability of success differs from 0.75. [CONCLUSION]

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