Confidence Interval Worksheet with Sample Data MTH 160:Statistics
Read the following scenario and complete each of the problemsbelow:
A flashlight company claims that the new bulb in its heavy-dutyflashlight will average 246 hours of light. A statistics studentdecides that he/she wants to test this claim at a 5% level ofsignificance to determine if there is evidence to support theclaim. The student randomly selects and tests 15 flashlight bulbsand records how long the bulb lasts until it burns out. Assume thelife of a bulb is normally distributed. T
he data is in the table below
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hrs: 246 224 231 242 237 240 243 236 239 255 256 239 247 231253
A. The standard deviation of the population is 7.4 hours.Construct a 95% confidence interval for this study.
B. Same scenario, but the population’s standard deviation is notknown. Construct a 95% confidence interval for this study.
C. Write a statement comparing and contrasting the twoconfidence intervals and results.
Read the following scenario and complete each of the problemsbelow:
A new car manufacturing company has emerged and has claimed thatits new hybrid car, the Pusho, gets a better gas mileage than thehighest ranked Toyota Prius. Consumer Reports Magazine decides totest this claim at a 5% level of significance. Consumer Reportsrandomly selects 10 of each type of car, calculates the miles pergallon for each car in the study, and records the data in the tablebelow. Assume miles per gallon of the cars is normallydistributed.
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
A. Construct a 90% confidence interval for the difference in thegas mileage of Pusho and Prius.
B. Construct a 95% confidence interval for the difference in thegas mileage of Pusho and Prius.
C. Write a statement comparing and contrasting the twoconfidence intervals and the significance of having 0 in both ofthose intervals.
