Question

. farm sizes the average farm size in the united states is 444 acres. a random sample of 40 farms in oregon indicated a mean size of 430 acres, and the population standard deviation is 52 acres. at a 0.05, can it be concluded that the average farm in oregon differs from the national mean? use the p-value method.

Answer 1

Based on the p-value method, we can conclude that the average farm size in Oregon is statistically different from the national mean.

The Breakdown

Conducting a hypothesis test using the p-value method, to determine whether the average farm size in Oregon differs from the national mean

The null and alternative hypotheses:

Null Hypothesis (H0): The average farm size in Oregon is equal to the national mean (µ = 444 acres).

Alternative Hypothesis (Ha): The average farm size in Oregon differs from the national mean (µ ≠ 444 acres).

The test statistic (z-score) can be calculated using the formula:

z = (x - µ) / (σ / √n)

Where:

x = sample mean (430 acres)

µ = population mean (444 acres)

σ = population standard deviation (52 acres)

n = sample size (40 farms)

Plugging in the values, we get:

z = (430 - 444) / (52 / √40)

z = -14 / (52 / √40)

z ≈ -2.13

Using a standard normal distribution table or a statistical software, we find that the p-value for a two-tailed test with a z-score of -2.13 is approximately 0.033.

Since the p-value (0.033) is less than the significance level (0.05), we reject the null hypothesis. This means that there is sufficient evidence to conclude that the average farm size in Oregon differs from the national mean.