Question

For safety reasons, calf dehorning has become a routine practice at dairy farms. A report by a continental government organization stated that 80% of that continent's dairy farms carry out calf dehorning. A later study, published in a reputable dairy science journal, found that in a sample of 641 dairy farms in the continent, 526 dehorn calves. Does the journal's study support or refute the figure reported by the government organization? Explain. Test the relevant hypotheses using a = 0.05.

Answer 1

The journal's study does not provide sufficient evidence to refute the figure reported by the government organization.

How to find evidence?

To determine whether the journal's study supports or refutes the figure reported by the government organization, we can perform a hypothesis test.

Null Hypothesis (H₀): The proportion of dairy farms in the continent that dehorn calves is 80%.

Alternative Hypothesis (H₁): The proportion of dairy farms in the continent that dehorn calves is different from 80%.

Significance Level (α):

0.05

Sample Proportion (
`\hat p`):

526/641 = 0.820

Standard Error (SE):

`√((\hat p)(1 - \hat p) / n) = √((0.820)(1 - 0.820) / 641) = 0.029`

Test Statistic (z):

`(\hat p - p_0) / SE` = (0.820 - 0.800) / 0.029

= 0.689

Now, compare the test statistic (z) to the critical values for the significance level (α) of 0.05.

For a two-tailed test, find the critical values that correspond to the area in both tails of the standard normal distribution that is equal to α/2 = 0.025. These critical values are approximately -1.96 and 1.96.

Since the test statistic (0.689) is within the range of the critical values (-1.96, 1.96), we fail to reject the null hypothesis.

Conclusion:

The journal's study does not provide sufficient evidence to refute the figure reported by the government organization. The sample proportion (0.820) is not significantly different from the hypothesized proportion (0.800). Therefore, we cannot conclude that the proportion of dairy farms in the continent that dehorn calves is different from 80%.