A Calgary observatory records daily the mean counting rates for cosmic rays for that specific day (data from the National Geophysical Data Center). These recorded values are approximately normally distributed. If, for a randomly selected sample of the observatory's records,  = 3455, and s = 126.7, test the claim that the mean for daily counting rates is actually equal to 3465.5.
Use the traditional approach summarized. Draw a graph showing the test statistic and critical values. In each case, assume that the population has a distribution that is approximately normal and that the sample is randomly selected.