Question

1. A study found the body temperatures of 16 healthy adults. The sample had a mean of 98.2 degrees and standard deviation was 0.62 degrees. Find the margin of error EBMand the 95% confidence interval for μ.

2. People have died in boat and aircraft accidents because an obsolete estimate of the mean weight of menwas used. In recent decades, the mean weight of men has increased considerably, so we need to update our estimate of that mean so that boats, aircraft, elevators, and other such devices do not become dangerously overloaded. A simple random sample was obtained: n= 40 and x= 172.55 lb. Research from several other sources suggests that the population of weights of men has a standard deviation given by σ= 26 lb.Find the 95% confidence interval for the mean.

3. A common claim is that garlic lowers cholesterol levels. In a test of the effectiveness of garlic, 49 subjects were treated with doses of raw garlic, and their cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol (in mg/dL) have a mean of 0.4 and a standard deviation of 21.0.

a.Use the sample statistics of n= 49, x= 0.4 and s= 21.0 to construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment.

b.What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?

Answer 1

1)

Answer)

As the population standard deviation is unknown here we will use t distribution table to estimate the interval

Degrees of freedom is = n-1 = 15

For 15 dof and 95% confidence level, critical value t from t table is = 2.13

Margin of error (MOE) = t*s.d/√n = 2.13*0.62/√16 = 0.33

Interval is given by

(Mean - MOE, Mean + MOE)

[97.87, 98.53].

You can be 95% confident that the population mean (μ) falls between 97.87 and 98.53.