Question

The body weight of a healthy 3-month-old colt should be about μ = 64 kg. (a) If you want to set up a statistical test to challenge the claim that μ = 64 kg, what would you use for the null hypothesis H0? μ > 64 kg μ < 64 kg μ = 64 kg μ ≠ 64 kg (b) In Nevada, there are many herds of wild horses. Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than 64 kg. What would you use for the alternate hypothesis H1? μ > 64 kg μ < 64 kg μ = 64 kg μ ≠ 64 kg (c) Suppose you want to test the claim that the average weight of such a wild colt is greater than 64 kg. What would you use for the alternate hypothesis? μ > 64 kg μ < 64 kg μ = 64 kg μ ≠ 64 kg (d) Suppose you want to test the claim that the average weight of such a wild colt is different from 64 kg. What would you use for the alternate hypothesis? μ > 64 kg μ < 64 kg μ = 64 kg μ ≠ 64 kg (e) For each of the tests in parts (b), (c), and (d), respectively, would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean? left; right; both left; both; right right; left; both both; left; right

Answer 1

The body weight of a healthy 3-month-old colt should be about μ = 64 kg.

(a) If you want to set up a statistical test to challenge the claim that μ = 64 kg,

the null hypothesis H₀   = 64 kg

b) In Nevada, there are many herds of wild horses.

Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than 64 kg.

Alternate hypothesis H₁ < 64 kg

(c) Suppose you want to test the claim that the average weight of such a wild colt is greater than 64 kg.

Alternate hypothesis   > 64 kg

(d) Suppose you want to test the claim that the average weight of such a wild colt is different from 64 kg.

Alternate hypothesis : 64 kg

(e) For each of the tests in parts (b), (c), and (d), respectively, would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean

left; right; both

Explanation for Hypothesis:

The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

Null hypothesis (H₀)

The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.

Alternative Hypothesis (H₁)

The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

One-sided and two-sided hypotheses

The alternative hypothesis can be either one-sided or two sided.

Two-sided

Use a two-sided alternative hypothesis (also known as a nondirectional hypothesis) to determine whether the population parameter is either greater than or less than the hypothesized value. A two-sided test can detect when the population parameter differs in either direction, but has less power than a one-sided test.

One-sided

Use a one-sided alternative hypothesis (also known as a directional hypothesis) to determine whether the population parameter differs from the hypothesized value in a specific direction. You can specify the direction to be either greater than or less than the hypothesized value. A one-sided test has greater power than a two-sided test, but it cannot detect whether the population parameter differs in the opposite direction.

P-Value

For Left tailed test : H₁: < 64 kg

P-Value = P(Z < Value of the test statistic) i.e area on left side of the mean

For Right tailed test: H₁ > 64 kg

P-Value = P(Z > Value of the test statistic) i.e area on right side of the mean

For Two tailed test : H₁ 64 kg

P-value = P(Z< - Value of the test statistic) + P(Z >  Value of the test statistic) i.e both sides of the mean