Problem Solving Example: The Mean Hemoglobin Levels of Vegans and Vegetarians

Research Scenario

Hemoglobin levels (g/dL) from the general population of adult men form a normal distribution with = 15.3 and = 0.95. Several studies have shown that vegans and vegetarians suffer from lower than normal hemoglobin levels, which indicates anemia. Using clinical data, a researcher measured hemoglobin levels from a sample of n = 100 adult men who followed a vegan or vegetarian diet. The average hemoglobin level (g/dL) for this sample was x = 13.2. Do these data indicate that following a vegan or vegetarian diet has a significant effect on hemoglobin levels? Test with p=.05.

Note

u = population mean

x = sample mean

= standard deviation

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Note: Each response is worth 6 points

Step 1: Set up your hypothesis and determine the level of significance

State the null hypothesis

In written format

Answer: There is no difference between the mean hemoglobin levels of vegans and vegetarians adult men and the mean hemoglobin levels of general population of adult men.

In mathematical format

Answer: The null hypothesis is H0: m = 15.3

State the alternative hypothesis

In written format

Answer: The mean hemoglobin levels of vegans and vegetarians adult men is less than the mean hemoglobin levels of general population of adult men.

In mathematical format

Answer: The alternative hypothesis is HA: m < 15.3.

Determine the Level of significance

Based on information in the scenario, what is the level of significance to be used?

Answer: 0.05.

Step 2: Select the appropriate test statistic

The appropriate test statistic for the above scenario is the one-sample z test. What is a Z test? Describe why this is the appropriate test for the scenario?

Answer: A Z-test is a hypothesis test based on the Z-statistic. The Z-test is assumed to have a standard normal distribution under the null hypothesis. The Z-test is appropriate for this scenario because the sample size is greater than 30. Additionally, it is appropriate because the population mean, the sample mean, and the populations standard deviation are known.

Step 3: Set up the decision rule

Based on the level of significance you set in Step 1 (Question 5) and whether your alternative hypothesis is directional or non-directional, what is your decision rule? (In other words, what is your rejection region?)

Answer: The alternative hypothesis is directional because it specifies the direction of the tested relationship. In this case, the alternative hypothesis predicts that vegans and vegetarians diets lead to lower than normal hemoglobin levels.

Step 4: Compute the test statistic

Calculate the z statistic. Please show your work.

Answer:

ZSTAT = (X-u) / dn = (13.2-15.3) / (0.96/100)

= -21.875

Step 5: Conclusion

Do you reject or fail to reject the null hypothesis?

Answer:

The critical region approach indicates null hypothesis should be rejected at the a = 0.05 level if Z < 1.65. Therefore, the null hypothesis is rejected because Z = -21.875 < 1.65, and therefore lies in the rejection region.

Are hemoglobin levels affected by a vegan or vegetarian diet?

Answer: The mean hemoglobin levels of vegans and vegetarians adult men is less than the mean hemoglobin levels of general population of adult men.