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# Cumulative weight loss: propranolol treatment

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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.

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#### Solution Preview

Please see the attachments.

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.
The 95% confidence interval is given by , where = 173, s = 27, n = 30, = 2.045229611

That is,

= (162.92, 183.08)

Thus with 95% confidence we can claim that the population mean weight loss for the propranolol group is within (162.92, 183.08) grams.
Details
Confidence Interval Estimate for the Mean

Data
Sample Standard Deviation 27
Sample Mean 173
Sample Size 30
Confidence Level 95%

Intermediate Calculations
Standard Error of the Mean 4.929503018
Degrees of Freedom 29
t Value 2.045229611
Interval Half Width 10.081965540

Confidence Interval
Interval Lower Limit 162.9180345
Interval Upper Limit 183.0819655

b) Provide a 95% confidence interval for the mean weight loss for the control group.
The 95% confidence interval is given by , where = 153, s = 26, n = 60, = 2.000995361

That is,

= (146.28, 159.72)

Thus with 95% confidence we can claim that the population mean weight loss for the control group is within (146.28, 159.72) grams.
Details
Confidence Interval Estimate for the Mean

Data
Sample Standard Deviation 26
Sample Mean 153
Sample Size 60
Confidence Level 95%

Intermediate Calculations
Standard Error of the Mean 3.356585567
Degrees of Freedom 59
t Value 2.000995361
Interval Half Width 6.716512148

Confidence Interval
Interval Lower ...

#### Solution Summary

Cumulative weight loss for propranolol treatment is examined. The mean loss weight compared between treatment and control for 90 patients during insulin-induced hypoglycemia is determined.

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