Question

1. a scientific report says that the proportion of the population that is left - handed is 0.10 with a margin of error of 0.02.

a. is 0.07 a plausible estimate for the proportion of the population that is left - handed? explain your reasoning.
b. is 0.087 a plausible estimate for the proportion of the population that is left - handed? explain your reasoning.
c. is 0.128 a plausible estimate for the proportion of the population that is left - handed? explain your reasoning.

1. a restaurant offers 5 appetizers that the manager thinks sell equally well. after looking over the sales for the previous month, the percentages of sales are:

bruschetta: 17% pesto bread: 22% spinach dip: 21% meatballs: 23% sampler: 17%
based on these results, is the manager’s thinking accurate? explain your reasoning.

Explanation:

Step1: Calculate confidence interval

$$0.10 - 0.02 = 0.08$$
$$0.10 + 0.02 = 0.12$$
Interval: $(0.08, 0.12)$

Step2: Check 0.07 against interval

0.07 < 0.08, outside interval.

Step3: Check 0.087 against interval

0.08 < 0.087 < 0.12, inside interval.

Step4: Check 0.128 against interval

0.128 > 0.12, outside interval.

Step5: Analyze appetizer sales

Equal sales mean 20% each.
All values (17%,22%,21%,23%,17%) are close to 20%, with small deviations likely due to random variation.

Answer:

a. No, 0.07 is not plausible.
b. Yes, 0.087 is plausible.
c. No, 0.128 is not plausible.
For question 5: Yes, the manager's thinking is accurate.