Question

Problem 2) Should you buy generic rather than brand-name batteries? A statistics student designed a study to see if generics perform differently than brand name batteries. He kept a battery-powered CD player continuously playing the same CD, with the volume control fixed at 5, and measured the time until no more music was heard through the headphones. He measured the time in minutes until the sound stopped. The data for 6 randomly selected batteries from a well-known brand and 6 randomly selected batteries from a generic brand are in the excel file, tab batteries. Based on other experiments, it is known that multiple measures of times for a brand of battery are approximately normally distributed.

a) For one experimental unit, what is the response variable? Categorical or quantitative? b) Verify the two conditions for inference:  2 independent random samples?  is n1 ≥ 30 or are the data approximately normally distributed or have no extreme asymmetry or outliers? Is n2 ≥ 30 or are the data approximately normally distributed or have no extreme asymmetry or outliers? c) Fill in the table with the summary statistics using Excel or StatKey (NOT by hand) for each group. Designate which is Group 1 and 2

BatteryType Times

BrandName 190.7

BrandName 203.5

BrandName 212.3

BrandName 206.5

BrandName 222.5

BrandName 209.4

Generic 194

Generic 188

Generic 199.2

Generic 172.4

Generic 184

Generic 169.5

d) Conduct a 4-step significance test to determine if there is evidence of a difference in performance of generic and brand name batteries. Be sure to state the conclusion in the context of the problem, not statistics jargon.

e) Calculate a 95% confidence interval and interpret in the context of the problem. Remember that with a quantitative response variable, a 95% confidence interval leads to a two-tailed significance test with α = 0.05 as our cutoff. If we reject Ho, then we would not expect µ0 to be inside the confidence interval. Look at your confidence interval. Does it contain the value for µ0? Look at the conclusion of the significance test. Are they consistent?

Answer 1