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Hypothesis testing and significance test for hypoglycaemia

Rachel's doctor suspects she is suffering from hypoglycaemia. The amount of glucose in the bloodstream varies and a person with hypoglycaemia has an average blood glucose level of less than 65 mg/dL. To determine whether Rachel is indeed hypoglycaemic the doctor sends her home with a glucose monitor to test her blood at 40 random times throughout the week.

a. Set up hypotheses to help determine if Rachel is hypoglycaemic.
b. Why did her doctor have her test her blood glucose level 40 times?
c. What would a Type I error be in the context of this situation?
d. What would a Type II error be in the context of this situation?
e. The results from the week of testing were x = 60.5mg/dL and s = 12.3 mg/dL. Conduct a significance test and give Rachel a diagnosis about hypoglycaemia.

Solution Preview

a. Set up hypotheses to help determine if Rachel is hypoglycaemic.
The null hypothesis tested is:
H0: Mean blood glucose level of Rachel in the week ≥ 65 mg/dL (µ ≥ 65)

The alternative hypothesis is
H1: Mean blood glucose level of Rachel in the week < 65 mg/dL (µ < 65)

b. Why did her doctor have her test her blood glucose level 40 times?
As the ...

Solution Summary

Hypothesis testing and significance test for hypoglycaemia

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