Question

Indicate the type of hypothesis each of the following are by

indicating directional or non-directional AND null or
alternative:

Answer 1

1.
`\(H_0: \mu_1 = \mu_2\), \(H_a: \mu_1 \\eq \mu_2\)` - This is a non-directional and two-tailed hypothesis test.

2.
`\(H_0: \mu \geq 50\), \(H_a: \mu < 50\)` - This is a directional and left-tailed hypothesis test.

3.
`\(H_0: \sigma_1 = \sigma_2\)`,
`\(H_a: \sigma_1 \\eq \sigma_2\)` - This is a non-directional and two-tailed hypothesis test.

4.
`\(H_0: p = 0.25\), \(H_a: p > 0.25\)` - This is a directional and right-tailed hypothesis test.

Step-by-step explanation:

In the first scenario,
`\(H_0: \mu_1 = \mu_2\)` and
`\(H_a: \mu_1 \\eq \mu_2\)` , it is a non-directional, two-tailed hypothesis test because it does not specify a particular direction of the difference between the population means
`(\(\mu\))`. The null hypothesis
`(\(H_0\))` assumes equality, while the alternative hypothesis
`(\(H_a\))` indicates inequality.

In the second case,
`\(H_0: \mu \geq 50\)` and
`\(H_a: \mu < 50\)`, it is a directional, left-tailed hypothesis test. The null hypothesis
`(\(H_0\))` states that the population mean
`(\(\mu\))` is greater than or equal to 50, and the alternative hypothesis
`(\(H_a\))` suggests that the population mean is less than 50.

Moving on to the third scenario,
`\(H_0: \sigma_1 = \sigma_2\` and
`\(H_a: \sigma_1 \\eq \sigma_2\)`, it is a non-directional, two-tailed hypothesis test for comparing the population standard deviations
`(\(\sigma\))`.

Lastly, in the fourth case,
`\(H_0: p = 0.25\)` and
`\(H_a: p > 0.25\)`, it is a directional, right-tailed hypothesis test. The null hypothesis
`(\(H_0\))` posits that the population proportion (p) is equal to 0.25, while the alternative hypothesis
`(\(H_a\))` suggests that the population proportion is greater than 0.25.