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

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