Tests of μ, Standard Deviation Known (3 of 4)

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  1. In step five, the probability computed in Step 4 is compared to the significance level stated in Step 2. Since the probability value (0.028) is less than the significance level (0.05) the effect is statistically significant.

  2. Since the effect is significant, the null hypothesis is rejected. It is concluded that the mean anxiety score of 10-year-old children with alcoholic parents is higher than the population mean.

  3. The results might be described in a report as follows:
    The mean score of children of alcoholic parents (M = 8.1) was significantly higher than the population mean ( µ= 7.0), z = 2.2, p = 0.028.

Summary of Computational Steps
  1. Specify the null hypothesis and an alternative hypothesis.

  2. Compute M = ΣX/N.

  3. Compute = .

  4. Compute where M is the sample mean and µ is the hypothesized value of the population.

  5. Use a z table to determine p from z.

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