Question

A student measuring how gasoline prices change records the cost of gas at 10 randomly selected stations in her hometown. One week​ later, she records the price again at the same 10 stations. She wants to estimate the mean price increase and subtracts week 2 from week 1. Her​ 90% confidence interval is ​(minus​$0.23,minus​$0.06). What can she​ conclude?

A. It cannot be concluded whether one is higher than the other.
B. These are both negative numbers so the week 2 prices are on average higher than the week 1 prices.
C. These are both negative numbers so the week 2 prices are on average lower than the week 1 prices.

Answer 1

The negative numbers in the 90% confidence interval (minus$0.23, minus$0.06) imply that there was an average decrease in gasoline prices from week 1 to week 2.

Step-by-step explanation:

Considering the 90% confidence interval for the mean price increase of gasoline (minus$0.23, minus$0.06), we can conclude that the average price of gas during week 2 is on average lower than during week 1. This is because both numbers in the interval are negative, which indicates that the mean price change from week 1 to week 2 is a decrease. If the interval contained positive values, it would suggest an increase in the prices. Since the interval does not contain zero, we can be 90% confident that there was a true mean decrease in the price of gasoline over this interval.

The student can conclude that the week 2 prices are on average lower than the week 1 prices because the confidence interval is negative. The confidence interval is a range of values within which the true population mean is likely to fall. In this case, the confidence interval is (-$0.23, -$0.06), indicating that the mean price increase is expected to be between -$0.23 and -$0.06.