Question

A laboratory believes that its equipment needs adjustment when the standard deviation of five samples of a known concertation exceeds 5.5mg/l. During one test, the following sample measurements wore recorded: 52.7, 55.2, 49.3, 53.0, and 62.4mg/L. Does a confidence interval suggest that the equipment requires adjustment? Explain

Answer 1

= (52.7 + 55.2 + 49.3 + 53 + 62.4)/5 = 54.52

s = sqrt(((52.7 - 54.52)^2 + (55.2 - 54.52)^2 + (49.3 - 54.52)^2 + (53 - 54.52)^2 + (62.4 - 54.52)^2)/4) = 4.88

For 95% confidence level, the critical values are

The 95% confidence interval for population standard deviation is

Since the interval contains 5.5, so the equipment does not require adjustment.