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A researcher selects a sample of sixteen individuals from a normal population with a mean of...

  1. A researcher selects a sample of sixteen individuals from a normal population with a mean of µ = 40 and σ = 8. A treatment is administered to the sample and, after treatment, the sample mean is 43. If the researcher uses a hypothesis test to evaluate the treatment effect, what z-score would be obtained for this sample (z-test value obtained)?
  2. Does the scenario Question #1 described a directional test? What would be the critical value for comparison? (Use α = .05.)
  3. Draw a normal distribution curve and label the values from question #1 (z­obt­) and question #4 (z­cv­).
  4. If you compare the mean values in the normal distribution above, what does this indicate about the difference between the means between the treatment sample and the population?

Math   Statistics-And-Probability   
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Answer #1

The test statistic is

  

No, it is not a directional test.

At = 0.05, the critical values are +/- z0.025 = +/- 1.96

Since the test statistic value is not in the critical region, so we should not reject the null hypothesis .

So we cannot conclude that there is a difference between the means between the treatment sample and the population.

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