State the null hypothesis, Ho, and the alternative...

State the null hypothesis, $H_{o},$ and the alternative hypothesis, $H_{a},$ that would be used for a hypothesis test for each of the following statements: a. The mean age of the youths who hang out at the mall is less than 16 years. b. The mean height of professional basketball players is greater than $6 \mathrm{ft} 6$ in. c. The mean elevation drop for ski trails at eastern ski centers is at least 285 feet. d. The mean diameter of the rivets is no more than 0.375 inch. e. The mean cholesterol level of male college students is different from $200 \mathrm{mg} / \mathrm{dL}$

State the null hypothesis, $H_{o},$ and the alternative hypothesis, $H_{a},$ that would be used for a hypothesis test for each of the following statements:
a. The mean age of the youths who hang out at the mall is less than 16 years.
b. The mean height of professional basketball players is greater than $6 \mathrm{ft} 6$ in.
c. The mean elevation drop for ski trails at eastern ski centers is at least 285 feet.
d. The mean diameter of the rivets is no more than 0.375 inch.
e. The mean cholesterol level of male college students is different from $200 \mathrm{mg} / \mathrm{dL}$

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Key Concepts

One-Tailed Test

A one-tailed test is used when the alternative hypothesis predicts a specific direction of the effect (either greater than or less than a given value). It focuses on detecting an effect in only one direction, making the statistical test more powerful for that direction of deviation.

Two-Tailed Test

A two-tailed test is employed when the alternative hypothesis does not specify a direction for the difference or effect, only that a difference exists. This type of test looks for deviations on both sides of the null hypothesis value and is used when the effect could be either greater or less than the stated parameter.

Null Hypothesis

The null hypothesis is a statement of no effect or no difference that serves as a default assumption to be tested. It represents the status quo or a specific value of the population parameter and is assumed to be true until evidence suggests otherwise.

Alternative Hypothesis

The alternative hypothesis is a statement that contradicts the null hypothesis and represents the effect or difference that the researcher is trying to support. It specifies the direction of the deviation from the null hypothesis or the existence of a difference.

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