In 2010 36 of Americans were considered obese A recent study

In 2010, 36% of Americans were considered obese. A recent study was done and found that 390 out of 1000 people surveyed we classified as obese. We are interested in determining whether or not there has been a significant increase in the percentage of Americans who are obese. Use =.01.

               a. What are the null and alternative hypotheses?

               b. What is the critical value?

               c. Calculate the test statistic.

               d. Find the p-value.

               e. What conclusion is made here?

               f. If we change to .10, would it change the conclusion you make here?

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.36
Ha:   p   >   0.36 [ANSWER]

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b)

As alpha = 0.01, right tailed, using table/technology,

zcrit = 2.326347874 [ANSWER]

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c)

As we see, the hypothesized po =   0.36      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.39      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.015178933      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.976423538   [ANSWER]

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d)  
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.024053414   [ANSWER]

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e)  

As P > 0.01, we failt to reject Ho. There is no significant increase in the percentage of Americans who are obese.

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f)

If alpha = 0.10, then as P < 0.10, we reject Ho. [The decision changed.]

There is significant increase in the percentage of Americans who are obese. [ANSWER]