Testing Claim about a Proportion For questions 9 10 11 use f

Testing Claim about a Proportion.

For questions 9, 10, 11 use following data:

Evaluate the claim that percent of small businesses closed this year (population proportion) is greater than 26%. Sample of 500 small businesses were taken all over the country and 145 of them were closed this year.   

H₀ – population proportion p = 0.26
H₁ – population proportion p > 0.26

Calculate z-value for test statistics

Use attached Table A-2 for Normal Distribution to find p-value.
At the significance level 0.05 make decision: reject or do not reject H₀.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.26
Ha:   p   >   0.26

As we see, the hypothesized po =   0.26      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.29      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.01961632      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.529338857 = 1.53 [ANSWER, Z VALUE]

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As this is a    1   tailed test, then, getting the p value,  
          
p =    0.0630
      
significance level =    0.05      

Comparing p <0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.   [DO NOT REJECT HO]