Answer Happy

5. [20 points] A company provides portable walkies-talkies to construction crews. They use batteries that last, on average, 55 hours of continuous use. The purchasing manager receives a brochure advertising a new brand of batteries with a lower price, but suspects that the lifetime of the batteries may be shorter than the brand currently in use. To test this, the new brand is installed in 8 randomly selected radios. A histogram of the data was approximately unimodal and symmetric. Here are the results for the lifetime of batteries (in hours): 46 53 57 56 52 59 49 53 a) [2 points] Find the mean and standard deviation of the sample using your calculator. b) [8 points] Find a 95% confidence interval for the true population mean. c) [10 points] Is there sufficient evidence to conclude that the purchasing manager is correct in his conjecture that the new brand has a shorter average lifetime? State and test an appropriate hypothesis using a significance level of a = 0.025.