Question

In a​ survey, 41​% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too​ high, so sheshe randomly selected 170 pet owners and discovered that 67 of them spoke to their pet on the telephone. Does the veterinarian have a right to be​ skeptical? Use the α=0.01 level of significance.

Answer 1

H0: p >= 0.41

Ha: p < 0.41

Sample proportion = 67 / 170 = 0.3941

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= ( 0.3941 - 0.41) / sqrt ( 0.41 ( 1 - 0.41) / 170 ]

= -0.42

From Z table,

z-critical value at 0.01 significance level = -2.326

Since test statistics > -2.326, fail to reject H0.

We conclude that we do not have sufficient evidence to support the claim