Question

the weight of the average 6th grade boy is 89 lbs. the principal of the school feeds them steak for first semester to see if their weight changes. what are the null and alternate hypotheses?
ho: μ = 89
h₁: μ = 89
ho: μ = 89
h₁: μ ≠ 89
ho: μ = 89
h₁: μ < 89
ho: μ = 89
h₁: μ > 89

Explanation:

Step1: Recall null and alternate hypotheses

The null hypothesis \(H_0\) is a statement of no change or equality. The alternate hypothesis \(H_1\) is what we are trying to find evidence for. Here, we want to see if the weight changes (not just stays the same).

Step2: Analyze each option

• Option 1 (\(H_0:\mu = 89\), \(H_1:\mu = 89\)): Both hypotheses are the same, which is incorrect as \(H_0\) and \(H_1\) should be different.
• Option 2 (\(H_0:\mu = 89\), \(H_1:\mu

eq89\)): \(H_0\) is the equality (no change) and \(H_1\) is the change (weight is different), which is correct for testing if weight changes.

• Option 3 (\(H_0:\mu = 89\), \(H_1:\mu < 89\)): This only tests for weight decreasing, not just any change.
• Option 4 (\(H_0:\mu = 89\), \(H_1:\mu>89\)): This only tests for weight increasing, not just any change.

Answer:

\(H_0:\mu = 89\), \(H_1:\mu
eq89\) (the second option in the given list)