Question

In a​ survey, 37 ​% 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 210 pet owners and discovered that 72 of them spoke to their pet on the telephone. Does the veterinarian have a right to be​ skeptical? Use the alpha equals0.05 level of significance.

Because np₀(1-p₀) = 10, the sample size is 5% population size, and the sample the requirement for testing the hypothesis satisfied.

What are the null and alternative​ hypotheses?

Determine the test​ statistic, z₀.

Determine the critical​ value(s).​(Round to two decimal places as​ needed.)

.

Answer 1

(a)

n = 210

p₀ = 0.37

The sample size is at most 5% of population size.

So,

the requirement for testing the hypothesis satisfied.

(b)

H0: Null Hypothesis: P0.37

HA: Alternative Hypothesis: P < 0.37 (Claim)

(c)

p = Sample Proportion = 72/210 = 0.3429

Test Statistic is given by:

Z₀ = (0.3429 - 0.37)/0.0333

= - 0.81

(d)

= 0.05

From Table, critical value of Z = - 1.65