Suppose a random variable is hypothesized to be normally distributed with a mean of 0 and a standard deviation of 1. A random sample of 200 observations of the variable yields frequencies in the intervals listed in the table shown at the bottom of the page. Do the data provide sufficient evidence to contradict the hypothesis that x is normally distributed with m = 0 and s = 1? Use the technique developed in Exercise 13.71.
Table for Exercise 13.72

Exercise 13.71,
A statistical analysis is to be done on a set of data consisting of 1,000 monthly salaries. The analysis requires the assumption that the sample was drawn from a normal distribution. A preliminary test, called the (2 goodness-of-fit test, can be used to help determine whether it is reasonable to assume that the sample is from a normal distribution. Suppose the mean and standard deviation of the 1,000 salaries are hypothesized to be $1,200 and $200, respectively. Using the standard normal table, we can approximate the probability of a salary being in the intervals listed in the table in the next column. The third column represents the expected number of the 1,000 salaries to be found in each interval if the sample was drawn from a normal distribution with ( = $1,200 and ( = $200. Suppose the last column contains the actual observed frequencies in the sample. Large differences between the observed and expected frequencies cast doubt on the normality assumption.

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-2 sx< -1 Interval -1 sx<0 0sx<1 1sx<2 Frequency 20 61 77 26 Expected Probability Frequency Frequency 23 136 341 341 136 23 Observed Interval Less than $800 .023 .136 .341 341 .136 .023 26 146 361 311 143 13 $800 < $1,000 $1,000 < $1,200 $1,200 < $1,400 $1,600 or above