Read the following scenario and complete each of the problems below:

A flashlight company claims that the new bulb in its heavy duty flashlight will average 246 hours of light. A statistics student decides that he/she wants to test this claim at a 5% level of significance to determine if there is evidence to support the claim. The student randomly selects and tests 15 flashlight bulbs and records how long the bulb lasts until it burns out. Assume the life of a bulb is normally distributed. The data is in the table below:

trial 1 hrs 246 trial 2 hrs 224 trial 3 hrs 231 trial 4 hrs 242 trial 5 hrs 237 trial 6 hrs 240 trial 7 hrs 243 trial 8 hrs 236 trial 9 hrs 239 trial 10 hrs 255 trial 11 hrs 256 trial 12 hrs 239 trial 13 hrs 247 trial 14 hrs 231 trial 15 hrs 253

1. The standard deviation of the POPULATION is 7.4 hours. Construct a 95% confidence interval for this study.

2. Same scenario, but the population's standard deviation is not known. Construct a 95% confidence interval for this study.

3. Give a statement comparing and contrasting the two confidence intervals and results.

A new car manufacturing company has emerged and has claimed that its new hybrid car, the Pusho, gets a better gas mileage than the highest ranked Toyota Prius. Consumer Reports Magazine decides to test this claim at a 5% level of significance. Consumer Reports randomly selects 10 of each type of car, calculates the miles per gallon for each car in the study, and records the data in the table below. Assume miles per gallon of the cars is normally distributed.

pusho: 54.1, 52.4, 55.7, 49.7, 50.6, 48.9, 51.8, 54.5, 56.9, 49.8

prius: 53.2, 54.3, 49.8, 50.1, 50.5, 56.1, 47.8, 53.4, 56.8, 48.7

1. Construct a 90% confidence interval for the difference in the gas mileage of Pusho and Prius.

2. Construct a 95% confidence interval for the difference in the gas mileage of Pusho and Prius.

3. Give a statement comparing and contrasting the two confidence intervals and the significance of having 0 in both of those intervals.