You wish to compare fasting cholesterol levels of an immigrant population with t

Question

You wish to compare fasting cholesterol levels of an immigrant population with that of the US population, but you have no good data suggesting whether or not the cholesterol levels of that population are higher or lower than the general US population. You know that the US population mean fasting cholesterol level is 195 mg/dl.

Suppose that you measured the fasting cholesterol level in 100 subjects from the immigrant population, and calculated a sample mean X=183 mg/dl with a sample standard deviation s=41 mg/dl.

a) Is there are "significant difference" between the US population mean and the immigrant population sample mean? Answer the question after conducting a two sided hypothesis test at 5% significance level. Show all the steps, including the p-value.

b) Your lab partner analyzed the same data by constructing a 95% confidence interval. Did both of you reach the same conclusion? Explain!

Explanation / Answer

(a)

Data:     

n = 100    

= 195    

s = 41    

x-bar = 183    

Hypotheses:    

Ho: = 195    

Ha: 195    

Decision Rule:    

= 0.05    

Degrees of freedom = 100 - 1 = 99

Lower Critical t- score = -1.9842169   

Upper Critical t- score = 1.9842169   

Reject Ho if |t| > 1.9842169   

Test Statistic:    

SE = s/n = 41/100 = 4.1   

t = (x-bar - )/SE = (183 - 195)/4.1 = -2.92683

p- value = 0.004247885    

Decision (in terms of the hypotheses):   

Since 2.926829268 > 1.984217 we reject Ho and accept Ha

Conclusion (in terms of the problem):   

There is a significant difference between the US population mean and the immigrant population mean

(b)

n = 100     

x-bar = 183     

s = 41     

% = 95     

Standard Error, SE = s/n =    41/100 = 4.1

Degrees of freedom = n - 1 =   100 -1 = 99   

t- score = 1.9842169     

Width of the confidence interval = t * SE =     1.98421690022499 * 4.1 = 8.135289291

Lower Limit of the confidence interval = x-bar - width =      183 - 8.13528929092247 = 174.8647107

Upper Limit of the confidence interval = x-bar + width =      183 + 8.13528929092247 = 191.1352893

Since 195 lies outside the above interval, we reject Ho and accept Ha

There is a significant difference between the US population mean and the immigrant population mean.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.