Question

1.In asurvey, 36% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be toohigh, so she randomly selected 240 pet owners and discovered that 78 of them spoke to their pet on the telephone. Does the veterinarian have a right to beskeptical? Use the alphaequals0.05 level of significance. Find the teststatistic, z 0? Find theP-value? Does the veterinarian have a right to beskeptical? A. The veterinarian does not have a right to be skeptical. There is not sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 36%. B. The veterinarian does not have a right to be skeptical. There is not sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is 36%. C. The veterinarian has a right to be skeptical. There is sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is not 36%. D. The veterinarian has a right to be skeptical. There is sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 36%

Answer 1

Here the hypothesis the veterinarian want to test is

H0:The veterinarian does not have a right to be skeptical

against H1: The veterinarian has right to be skeptical.

i.e. H0: p=0.36 VS H1: p<0.36

The test statistic for this test is,

here p^ =78/240=0.325

the calculated value of test statistics is

z=(0.325-0.36)/sqrt(0.36*0.64/240)

z= -1.12962

whereas, Z(0.05)= -1.644854

Since Zcal < Z(0.05)

hence we accept the Null Hypothesis

Conclusion: The Veterinarian does not have right to be Skeptical.

Also, P-value=P[p>0.36]=0.6405764

Since P-value is greater than 0.05 we accept H0 based on P-value criteria.

So the conclusion remains same i.e.The Veterinarian does not have right to be Skeptical.