Sue wants to know how many families in her small neighborhood of 50 homes would volunteer to help at a neighborhood animal shelter. She put all the addresses in a bag and drew a random sample of 25 addresses. She then asked those families if they would volunteer to help at the shelter. She found that 18% of the families would volunteer to help at the shelter. She claims that 18% of the neighborhood families would be expected to help at the animal shelter. Is this a valid inference? (1 point)

Question

Sue wants to know how many families in her small neighborhood of 50 homes would volunteer to help at a neighborhood animal shelter. She put all the addresses in a bag and drew a random sample of 25 addresses. She then asked those families if they would volunteer to help at the shelter. She found that 18% of the families would volunteer to help at the shelter. She claims that 18% of the neighborhood families would be expected to help at the animal shelter. Is this a valid inference? (1 point)

Answer 1

This is not a valid inference. A sample of 25 addresses may not be representative of the entire population of 50 homes. To make a valid inference, Sue would need to conduct a larger and more representative survey of the neighborhood families.

Answer 2

To determine if Sue's inference is valid, we can use statistical testing.

Step 1: Hypothesis formulation:
- Null hypothesis (H0): The proportion of families in the neighborhood that would volunteer to help at the animal shelter is equal to 18%.
- Alternative hypothesis (H1): The proportion of families in the neighborhood that would volunteer to help at the animal shelter is not equal to 18%.

Step 2: Test statistic selection:
- Since we are comparing the proportion of families to a known value (18%), the appropriate test statistic to use is the z-test.

Step 3: Test statistic calculation:
- The formula to calculate the z-test statistic for proportions is:
z = (p̂ - p) / √(p * (1 - p) / n),
where p̂ is the sample proportion, p is the hypothesized proportion, and n is the sample size.

Step 4: Critical value determination:
- We need to determine the critical value(s) at the desired significance level (e.g., α = 0.05) from the standard normal distribution.

Step 5: Comparison:
- We compare the calculated test statistic to the critical value(s) to determine if we reject or fail to reject the null hypothesis.

If the calculated test statistic falls outside the critical region, we reject the null hypothesis and conclude that Sue's claim is not valid. If it falls inside the critical region, we fail to reject the null hypothesis, and Sue's claim remains valid.

Please provide me with the value of p̂, the sample proportion of families that would volunteer to help at the animal shelter, so I can continue with the calculations.