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# Hypothesis testing and significance test for hypoglycaemia

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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.

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#### 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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## Cumulative weight loss: propranolol treatment

The following table presents the mean cumulative weight loss (in grams) for 30 patients receiving propranolol (treatment) and for 60 control patients following sweating during insulin-induced hypoglycemia.

Mean loss weight compared between treatment and control for 90 patients during insulin-induced hypoglycemia
Intervention N Mean Weight Loss
(in grams) Standard Deviation
Propranolol 30 173 27.0
Control 60 153 26.0

(Note: you can assume equal variance for the two groups.)

a) Provide a 95% confidence interval for the mean weight loss for the propranolol group.
b) Provide a 95% confidence interval for the mean weight loss for the control group.
c) Provide the interpretation of the 95% confidence interval for the mean weight loss for the propranolol group.
d) Using a two-sided test, conduct a test of hypothesis and provide the details of this test. Do we have sufficient evidence to conclude that the mean cumulative weight loss is different for the two groups? (Use a type I error level of = 0.05)
e) Write your conclusion from (d) in words, as you would present them in a report of the findings to a group of biomedical researchers (who might or might not be as well-versed in biostatistics as you are :-).
f) Compute the mean weight loss difference between the propranolol and control group.
g) Provide a 95% confidence interval for the difference in mean weight loss between the propranolol and control group.
h) Provide the interpretation of the 95% confidence interval for the difference in mean weight loss between the propranolol and control group.
Perform the same hypothesis test as in (d) and (e), but change the type I error level to 0.01. How does your main result / conclusion change? (Do not forget your one-two sentence interpretation.)

a) What is the possible alternative?

b) Why do you think we suggested using a two-sided test instead of that alternative?

c) Conduct the test with the possible alternative.