A consumer agency has retained an independent testing firm to examine a televisi

Question

A consumer agency has retained an independent testing firm to examine a television manufacturer’s claim that its 50-inch console model consumes just 110 watts of electricity. Based on a preliminary study, the population standard deviation has been estimated as 11.2 watts for these sets. In undertaking a larger study, and using a simple random sample, how many sets must be tested for the firm to be 95% confident that its sample mean does not differ from the actual population mean by more than 3.0 watts?

Explanation / Answer

Given that E = 3, = 11.2 and = 0.05

Z (/2) = 1.96 (From Z-tables)

The sample size is given by:-

n = (Z/2*/E) ²

n = (1.96*11.2/3)²

n = (7.317)²

n = 53.54 ~ 54

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