Question

a. In an American Animal Hospital Association survey, 37% of respondents stated that they talked to their pets on the telephone. A veterinarian found this result hard to believe, so he randomly selected 150 pet owners and discovered that 54 of them spoke to their pet on the telephone. At 0.05 significant level, test the result stated by the American Animal Hospital Association.

b. With a random sample 1026 adult Americans, 534 stated the amount of federal tax they have to pay is too high. Use 0.01 significant level to test the claim that at least half of Americans say federal tax is too high.

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.37
Alternative Hypothesis: p ≠ 0.37

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.36 - 0.37)/sqrt(0.37*(1-0.37)/150)
z = -0.25

P-value Approach
P-value = 0.8026
As P-value >= 0.05, fail to reject null hypothesis.

b)
Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.5
Alternative Hypothesis: p > 0.5

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.5205 - 0.5)/sqrt(0.5*(1-0.5)/1026)
z = 1.31

P-value Approach
P-value = 0.0951
As P-value >= 0.01, fail to reject null hypothesis.