Question

In a survey, 38% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too high, so he randomly selected 150 pet owners and discovered that 53 of them spoke to their pet on the telephone. Does the vet have a right to be skeptical? use the confidence interval .1 level of significance. a) because np0(1-p0)= blank (=, not equal, greater, or less than) 10, the sample size is (blank- less or greater) 5% of the population size and the sample (blank-) the requirements for testing the hypothesis (blank- are or are not) satisfied. b)what are the null and alternative hypotheses? c)determine the test statistic. d)determine the critical values. e) does the vet have a right to be skeptical?

Answer 1

Solution:-

a) Because np0(1-p0) is greater 10, the sample size is less than 5% of the population size and the sample requirements for testing the hypothesis are satisfied.

b) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.38
Alternative hypothesis: P < 0.38

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.03963
c)

z = (p - P) / S.D

z = - 0.673

d) zCritical = - 1.645

Rejection region is z < - 1.645

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 0.673.

Thus, the P-value = 0.2505

Interpret results. Since the z-value (- 0.673) does not lies in the rejection region, hence we failed to reject the null hypothesis.

e) No, the vet have a right to be skeptical.