Question

Suppose that measurements of cholesterol level in women in the U.S. population aged 21-40 is normally distributed with mean 54 mg/dL. It is desired to test if the cholesterol level among Asian immigrants is different from those in the general U.S. population. A study on a sample of 130 Asian women of age 21-40 yielded an average measurement of 55.06 with a standard deviation of 8.

The appropriate formulation of the testing problem is .
O H0 : μ ≤ 54, H1 : μ > 54
O H0 : μ ≥ 54, H1 : μ > 54
O H0 : μ = 54 ,H1 :u ≠ 54

Answer 1

The appropriate formulation of the hypothesis test to determine if the cholesterol level among Asian immigrants differs from the U.S. population is H0: μ = 54 and H1: μ ≠ 54, representing a two-tailed test.

Step-by-step explanation:

The question is concerned with hypothesis testing for a single population mean in the field of statistics. When formulating a hypothesis test to find out if the cholesterol level among Asian immigrants is different from the general U.S. population (whose mean is 54 mg/dL), it is important to define both the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis typically reflects the status quo or the claim to be tested, while the alternative hypothesis is what you want to prove.

Given that we are testing if there is a difference, not specifically if it is greater or lesser, we set up a two-tailed test. Therefore, the correct hypotheses formulation for this situation is:

• H0: μ = 54 (The population mean is equal to 54 mg/dL)
• H1: μ ≠ 54 (The population mean is not equal to 54 mg/dL)

If the sample mean significantly deviates from the population mean, either higher or lower, we may reject the null hypothesis.