According to the federal government, 24% of workers covered by their company\'s

Question

According to the federal government, 24% of workers covered by their company's health care plan were not required to contribute to the premium (Statistical Abstract of the United States: 2006). A recent study found that 81 out of 400 workers sampled were not required to contribute to their company's health care plan.

Develop hypotheses that can be used to test whether the percent of workers not required to contribute to their company's health care plan has declined.

H0: p Selectgreater than .24greater than or equal to .24equal to .24less than or equal to .24less than .24not equal to .24Item 1 {C}
Ha: p Selectgreater than .24greater than or equal to .24equal to .24less than or equal to .24less than .24not equal to .24Item 2 {C}

What is a point estimate of the proportion of workers who are not required to contribute to their company's health care plan (to 4 decimals)?

Has a statistically significant decline occurred in the proportion of workers who are not required to contribute to their company's health care plan? Use = 05.

Calculate the value of the test statistic (to 2 decimals).


What is the p-value (to 4 decimals)?


What is your conclusion?
SelectConclude the proportion of workers required to contribute has declinedDo not conclude the proportion of workers required to contribute has declinedItem 6

Explanation / Answer

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.24
Ha:   p   <   0.24 [ANSWER]

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b)

As we see, the hypothesized po =   0.24      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.2025   [ANSWER, POINT ESTIMATE]

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c)

Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.021354157      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.756098397   [ANSWER, TEST STATISTIC]

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d)  
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.039535804   [ANSWER, P VALUE]

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e)

  
significance level =    0.05      

As P < 0.05, REJECT THE NULL HYPOTHESIS.      

Hence,

OPTION A: Conclude the proportion of workers required to contribute has declined [ANSWER]

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