Short Answer 
The answer outlines a three-step process to compare the proportion of adults consuming at least 3 pounds of bacon in 2011 and 2016. It includes calculating sample proportions for both years, determining the pooled sample proportion as 0.23, and finding the test statistic z using the specified formula.
Step 1: Identify Sample Proportions
To compare the proportion of adults consuming at least 3 pounds of bacon in different years, we first need to determine the sample proportions for each year. For 2011, the sample proportion is 0.17, and for 2016, it is 0.25. Make sure to note the sample sizes, which are 200 for 2011 and 600 for 2016.
- 2011: p1 = 0.17
- 2016: p2 = 0.25
Step 2: Calculate Pooled Sample Proportion
The next step involves calculating the pooled sample proportion, denoted as p. This value is essential for determining the overall estimate of the proportion across both years. The formula for this calculation involves combining the counts from both years and dividing by the total sample size.
- Formula: p = (x1 + x2) / (n1 + n2)
- Where:
- x1 = 0.17 * 200 = 34
- x2 = 0.25 * 600 = 150
- Pooled Proportion: p = 184 / 800 = 0.23
Step 3: Calculate the Test Statistic
After obtaining the pooled proportion, the final step is to substitute the values into the test statistic formula for comparing the two proportions. This involves simplifying the equation to find the z value, which indicates the significance of the difference between these proportions. Use the values of the sample proportions and the pooled proportion to compute z.
- Test Statistic Formula: z = (p1 – p2) / sqrt(p * (1 – p) * (1/n1 + 1/n2))
- Substitute Values: z = (0.17 – 0.25) / sqrt(0.23 * 0.77 * (1/200 + 1/600))