Question

For each statement, select the correct null hypothesis (H0) and alternative hypothesis (H1) in symbolic form.

(a) the mean height of all adult American males is 69 inches (5 ft 9 in). a researcher wants to prove that young American males between the ages of 18 and 21 tend to be taller than 69 inches. a random sample of 100 young American males ages 18 to 21 yielded a sample mean of 71 inches.
Options:
Option 1: H0: μ = 69, H1: μ > 69
Option 2: H0: μ > 69, H1: μ = 69
Option 3: H0: μ = 71, H1: μ > 69
Option 4: H0: μ > 71, H1: μ = 69

Answer 1

Option 1 is the correct pair of hypotheses for the scenario with H0: μ = 69 and H1: μ > 69, the null hypothesis stating the mean height is 69 inches and the alternative that it's greater.

Step-by-step explanation:

For the given scenario, where a researcher wants to prove that young American males between the ages of 18 and 21 tend to be taller than 69 inches, the correct null hypothesis (H0) and alternative hypothesis (H1) in symbolic form would be Option 1:

H0: μ = 69, which states that the mean height of all adult American males is 69 inches.

H1: μ > 69, which states that the mean height of young American males aged 18 to 21 is greater than 69 inches.

This is because the null hypothesis typically represents a statement of 'no effect' or 'no difference,' which is being tested against the alternative hypothesis that there is an effect or a difference. Since the researcher's claim is about young males being taller, the alternative hypothesis should reflect a greater-than sign (>).