In a certain chemical process, it is very important that a particular solution that is to be used as a reactant have a pH of exactly 8.20. A method for determining pH that is available for solutions of this type is known to give measurements that are normally distributed with a mean equal to the actual pH and with a standard deviation of .02. Suppose 10 independent measurements yielded the following pH values:
(a) What conclusion can be drawn at the level of significance? (b) What about at the level of significance?
We are given sample of size . Calculate that the sample mean is
where is population mean. We are given that is population standard deviation. We know that test statistics has distribution
The -value of this random sample is
where is CDF of standard normal and we have used table of CDF of standard normal in appendix to obtain final answer. Since -value is less than significance levels in (a) and (b), we reject the null hypothesis in both cases.
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