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  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 deviations 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 above. 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 μ = $1,200 and ˆ‘ = $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.

a. Compute the 2 statistic based on the observed and expected frequencies-just as you did in Section 10.2.
b. Find the tabulated 2 value when α = .05 and there are 5 degrees of freedom. (There are k - 1 = 5 df associated with this 2 statistic.)
c. Based on the 2 statistic and the tabulated 2 value, is there evidence that the salary distribution is no normal?
d. Find an approximate observed significance level for the test in part c.

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Interval Probability Expected Frequency Observed Frequency Less than $800 Between $800 and $1,000 Between $1.000 and $1,200 Between $1.200 and $1.400 Between $1.400 and $1,600 Above $1,600 023 136 341 341 136 023 23 136 341 341 136 23 26 146 361 311 143 13