Consider the following hypothesis test H0 p 20 Ha p not equ

Consider the following hypothesis test:

H0: p = .20

Ha: p not equal to .20

A sample of 400 provided a sample proportion p-bar = .175.

a. Compute the value of the test statistic (to 2 decimals).

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

c. Using  = .05, can you conclude that the population proportion is not equal to .20? Yes or No

Answer the next three questions using the critical value approach.

d. Using  = .05, what is the critical value for the test statistic? (+ or -)

e. State the rejection rule: Reject H0 if z is _________ the lower critical value or ________ the upper critical value.

f. Using  = .05, can you conclude that the population proportion is not equal to .20? Yes or no.

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.2
Ha:   p   =/=   0.2

As we see, the hypothesized po =   0.2      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.175      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.02      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.25   [ANSWER]

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b)  
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.211299547   [ANSWER]

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c)

As P > 0.05, NO, we cannot conclude that the population proportion is not equal to .20. [ANSWER, NO]

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d)

As this is a two tailed test, then the critical values are

zcrit = +/- 1.96 [ANSWER]

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e)

Reject H0 if z is LESS THAN the lower critical value or GREATER THAN the upper critical value.

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f)

As -1.96<-1.25<1.96, then NO, we cannot conclude that the population proportion is not equal to .20. [NO]