Question

Let x be a hypothesized mean value. Select an appropriate type of hypothesis for the following: H0: μ ≥ x, Ha: μ < x?

1) One-tailed hypothesis test
2) Two-tailed hypothesis test
3) Null hypothesis
4) Alternative hypothesis

Answer 1

The appropriate type of hypothesis test for H0: μ ≥ x, Ha: μ < x is a one-tailed hypothesis test, specifically a left-tailed test because the alternative hypothesis indicates a mean less than the hypothesized value.

Step-by-step explanation:

The type of hypothesis test in the question where H0: μ ≥ x, Ha: μ < x is a one-tailed hypothesis test. Specifically, it is a left-tailed test because the alternative hypothesis Ha suggests that the mean is less than the hypothesized value x.

To further explain, in hypothesis testing:

• Null hypothesis (H0): This is a statement of no effect or no difference and is assumed to be true until evidence indicates otherwise.
• Alternative hypothesis (Ha): This is what you are trying to demonstrate, it posits that there is an effect or a difference.
• A one-tailed test is used when the alternative hypothesis is directional, indicating that the parameter of interest is either greater than or less than a certain value, but not both.
• A two-tailed test is used when the alternative hypothesis suggests the parameter is simply not equal to the hypothesized value, regardless of direction.

For example, if you believe a bottle of water contains less than the labeled amount, you would use a left-tailed test. However, if you are testing whether the mean is not equal to a certain value (neither greater nor lesser specifically), you would use a two-tailed test.