Question

Using a significance level of 0.10, what would you recommend to the winery? State the appropriate null and alternative hypotheses.

a) H0: p ≥ 0.25, Ha: p < 0.25
b) H0: p = 0.25, Ha: p ≠ 0.25
c) H0: p < 0.25, Ha: p ≥ 0.25
d) H0: p > 0.25, Ha: p ≤ 0.25

Answer 1

Using a significance level of 0.10, the winery should use a right-tailed test with H0: p ≤ 0.25 and Ha: p > 0.25. If the p-value is less than 0.10, the null hypothesis should be rejected.

Step-by-step explanation:

For a significance level of 0.10, the appropriate null hypothesis (H0) and alternative hypothesis (Ha) would be:

• H0: p ≤ 0.25
• Ha: p > 0.25

We are looking for evidence that the proportion (p) is greater than 0.25, hence a right-tailed test is suitable. The alternative hypothesis reflects this by indicating p > 0.25. If we obtain a p-value that is less than the significance level (0.10), we would reject the null hypothesis, indicating there is significant evidence that the proportion is greater than 0.25. Remember, the p-value represents the probability of obtaining a sample result as extreme as the one observed, assuming the null hypothesis is true.