Question 1181349
Here's how to conduct a hypothesis test to determine if the marketing campaign was effective:

**1. State the Hypotheses:**

*   **Null Hypothesis (H₀):** The percentage of males aged 20-39 who consume the recommended daily requirement of calcium has *not* increased. (p ≤ 0.489)
*   **Alternative Hypothesis (H₁):** The percentage of males aged 20-39 who consume the recommended daily requirement of calcium *has* increased. (p > 0.489)  This is a right-tailed test.

**2. Determine the Level of Significance:**

α = 0.10

**3. Calculate the Sample Proportion (p̂):**

p̂ = (Number who consume recommended calcium) / (Total number surveyed)
p̂ = 21 / 35
p̂ = 0.6

**4. Calculate the Test Statistic (z-score):**

We use a z-test for proportions because the sample size is large enough.

z = (p̂ - p) / sqrt[p(1-p)/n]
z = (0.6 - 0.489) / sqrt[(0.489 * 0.511) / 35]
z = 0.111 / sqrt(0.00714)
z = 0.111 / 0.0845
z ≈ 1.31

**5. Determine the Critical Value (or P-value):**

*   **Critical Value Approach:** For a right-tailed test with α = 0.10, the critical z-value is approximately 1.28 (you can find this using a z-table or calculator).  If our calculated z-score is greater than 1.28, we reject the null hypothesis.

*   **P-value Approach:** The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.  Since this is a right-tailed test, we want the area to the *right* of our z-score (1.31) on the standard normal distribution. Using a z-table or calculator, we find that the p-value is approximately 0.095.

**6. Make a Decision:**

*   **Critical Value Approach:** Our calculated z-score (1.31) is *greater* than the critical value (1.28). Therefore, we *reject* the null hypothesis.

*   **P-value Approach:** Our p-value (0.095) is *less than* our significance level (0.10). Therefore, we *reject* the null hypothesis.

**7. State the Conclusion:**

There *is* sufficient evidence at the α = 0.10 level of significance to conclude that the percentage of males aged 20 to 39 who consume the recommended daily requirement of calcium has increased after the marketing campaign.