Questions: Is the pair of hypotheses H0: μ ≤ 50, HA: μ>50 valid? A. No, because the parameter being tested is not a population parameter. B. No, because the alternative hypothesis does not include all population values that are not included in the null hypothesis. C. No, because the null hypothesis does not contain an equality sign. D. No, because the null hypothesis and alternative hypothesis contain population values that overlap. E. Yes, because the null hypothesis contains an equality sign and the alternative hypothesis includes all population values not included in the null hypothesis.

Is the pair of hypotheses H0: μ ≤ 50, HA: μ>50 valid?
A. No, because the parameter being tested is not a population parameter.
B. No, because the alternative hypothesis does not include all population values that are not included in the null hypothesis.
C. No, because the null hypothesis does not contain an equality sign.
D. No, because the null hypothesis and alternative hypothesis contain population values that overlap.
E. Yes, because the null hypothesis contains an equality sign and the alternative hypothesis includes all population values not included in the null hypothesis.

Transcript text: f. Is the pair of hypotheses $H_{0}: \mu \leq 50, H_{A}: \mu>50$ valid? A. No, because the parameter being tested is not a population parameter. B. No, because the alternative hypothesis does not include all population values that are not included in the null hypothesis. C. No, because the null hypothesis does not contain an equality sign. D. No, because the null hypothesis and alternative hypothesis contain population values that overlap. E. Yes, because the null hypothesis contains an equality sign and the alternative hypothesis includes all population values not included in the null hypothesis.

Solution

Solution Steps

Step 1: Analyzing the Hypotheses

We are given the pair of hypotheses:

Null Hypothesis: $ H_{0}: \mu \leq 50 $
Alternative Hypothesis: $ H_{A}: \mu > 50 $

To determine the validity of these hypotheses, we need to consider the requirements for a null hypothesis and an alternative hypothesis.

Step 2: Requirements for Null and Alternative Hypotheses

A valid null hypothesis should contain an equality sign, typically expressed as $ H_{0}: \mu = \mu_0 $ for some hypothesized value $ \mu_0 $. The alternative hypothesis should encompass all values not included in the null hypothesis.

In this case, the null hypothesis $ H_{0}: \mu \leq 50 $ does not contain an equality sign, which is a fundamental requirement.

Step 3: Evaluating the Options

We evaluate the provided options:

A. Incorrect, as the parameter being tested is indeed a population parameter.
B. Incorrect, as the alternative hypothesis does include values not in the null hypothesis.
C. Correct, because the null hypothesis does not contain an equality sign.
D. Incorrect, as the null and alternative hypotheses do not overlap.
E. Incorrect, as the null hypothesis does not contain an equality sign.