Question

In a​ survey, 33​% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too​ high, so she randomly selected 150 pet owners and discovered that 46 of them spoke to their pet on the telephone. Does the veterinarian have a right to be​ skeptical? Use the alphaequals0.01 level of significance. What are the null and alternative hypotheses?Use technology to find the P-Value.

Answer 1

p value =0.544

Explanation:

Given that in a survey, 33​% of the respondents stated that they talk to their pets on the telephone.

`H_0: p = 0.33\\H_a: p <0.33`

(left tailed test at 1% level)

Sample proportion p =
`(46)/(150) \\=0.3067`

Assuming H0 to be true, std error of proportion

=
`\sqrt{(0.33*0.67)/(150) } \\=0.0384`

p difference = -0.0233

Test statistic Z = p difference/std error

= -0.6067

p value = 0.544

Since p > alpha, we accept H0