Question

Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. For a random sample of 40 weekdays, daily parking income resulted in a histogram that was right-skewed. Working independent of one another, three city officials each obtained a different confidence interval. Each confidence interval corresponds to a different level of confidence; 90%, 95%, or 99%. Confidence Interval #1: (121.55, 130.45) Confidence Interval #2: (122.29, 129.71) Confidence Interval #3: (120.07, 131.93) Which interval corresponds to 90% confidence?

Answer 1

Here we have three confidence interval.

As we know that when confidence level is increased the width of the confidence interval is also increased.

Confidence Interval #1: (121.55, 130.45), Width=130.45-121.55=8.9

Confidence Interval #2: (122.29, 129.71) , Width=129.71-122.29=7.42

Confidence Interval #3: (120.07, 131.93) ,Width=131.93-120.07=11.89

Since  Confidence Interval #2: (122.29, 129.71) has the lowest width of the confidence interval . Hence this will be 90% confidence.

Confidence Interval #3: (120.07, 131.93) has highest width so this will be 99% confidence interval.

Confidence Interval #1: (121.55, 130.45) will be 95% confidence interval.