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 Find the mean and standard deviation of the sample using your calculator. Find a 95% confidence interval for the true population mean. 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 � = 0.025.

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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

  • Find the mean and standard deviation of the sample using your calculator.
  • Find a 95% confidence interval for the true population mean.
  • 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 � = 0.025.
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