In a survey 33 of the respondents stated that they talk to t

In a survey, 33% of the respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian believed this result to be too high, so he randomly selected 150 pet owners and discovered that 36 of them spoke to their pet on the answering machine or telephone. Does the veterinarian have a right to be skeptical? Use the a= 0.05 level of significance.

What are the null and alternative hypotheses?

Ho:p_____ versus H1:p_________

Does the veterinarian have a right to be skeptical?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.33
Ha:   p   <   0.33 [ANSWER]

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As we see, the hypothesized po =   0.33      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.24      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[p^(1 - p^)/n] =    0.038392708      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.344195175      
          
As this is a    1   tailed test, then, getting the p value,  
          

p =    0.01906819      

significance level =    0.05      

Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.

YES, THE VETERINARIAN HAVE A RIGHT TO BE SKEPTICAL AS THERE IS A SIGNFICANT EVIDENCE AT 0.05 SIGNIFICANCE THAT THE POPULATION PROPORTION IS LESS THAN 33%. [ANSWER]