Question

The distribution of blood cholesterol level in the population of all male patients tested in a large hospital over a 10-year period is close to Normal with mean 224 milligrams per deciliter (mg/dL) and standard deviation σ = 42 mg/dL. You measure the blood cholesterol of 14 male patients 20--34 years of age. The mean level is x = 195 mg/dL. Is the mean μ for all young men aged 20--34 who have been patients in the hospital different than that of the population of all male patients? State the hypotheses, compute the test statistic and P-value to answer the question. Use a 1% significance level. Assume that σ is the same as in the general population.

Answer 1

The null and alternative hypothesis for given significance level of is as follows:

i.e., the true mean blood cholesterol level in the population of young male patients aged 20-34 years is 224 mg/dL which is same as in the population of all male patients.

i.e., the true mean blood cholesterol level in the population of young male patients aged 20-34 years is different than 224 mg/dL, or different than the mean level in the population of all male patients.

Given:

sample of 14 male patients aged 20-34 years is given as-

sample size,

sample mean,

population standard deviation for all male aged 20-34 years which is same as the general male population i.e.

Test-statistic:    

The test-statistic is calculated as

P-value: Since we are testing a two-tailed hypothesis, so the p-value is given by-

Decision:   

                     

Since,

So, at 1% significance level the data does provide sufficient evidence to support the alternative hypothesis, i.e., . So we can conclude that, the true mean blood cholesterol level in the population of young male patients aged 20-34 years is different than 224 mg/dL, or we can say that it is different than the mean level in the population of all male patients.