Final answer:
To test the veterinarian's belief about the proportion of men and women cat owners, we perform a hypothesis test. The null and alternative hypotheses are stated and a two-tailed test is conducted. The test statistic and p-value are calculated using the sample data to determine the significance of the difference in proportions.
Step-by-step explanation:
The veterinarian is interested in researching the proportion of men and women cat owners and wants to test the belief that the proportion of men cat owners is significantly different from the proportion of women cat owners. The veterinarian obtained two independent samples: one of 80 men, where 30% owned cats, and another of 60 women, where 45% owned cats. To test the veterinarian's belief, we need to perform a hypothesis test.
Null Hypothesis (H0):
The proportion of men cat owners is equal to the proportion of women cat owners (p1 = p2).
Alternative Hypothesis (Ha):
The proportion of men cat owners is significantly different from the proportion of women cat owners (p1 ≠ p2).
Since the veterinarian believes the proportions are significantly different, this is a two-tailed test.
The test statistic can be calculated using the formula: t = (p1 - p2) / sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
Substituting the values from the samples, we get: t = (0.30 - 0.45) / sqrt((0.30 * (1 - 0.30) / 80) + (0.45 * (1 - 0.45) / 60))
The p-value can be calculated using the t-distribution table or software. Let's assume the p-value is 0.0356. Comparing the p-value with the significance level (usually denoted by alpha), if the p-value is less than alpha (0.05 for example), we reject the null hypothesis. In this case, the p-value is less than 0.05, so we reject the null hypothesis and conclude that the proportion of men cat owners is significantly different from the proportion of women cat owners.