Null and Alternative Hypotheses Some of the following...

Null and Alternative Hypotheses Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, $H_{0}$, and the alternative hypothesis. $H_{a}$, in terms of the appropriate parameter $(\mu \text { or } p)$. a. The mean number of years Americans work before retiring is 34. b. At most $60 \%$ of Americans vote in presidential elections. c. The mean starting salary for San Jose State University graduates is at least $\$ 100,000$ per year. d. Twenty-nine percent of high school seniors get drunk each month. e. Fewer than $5 \%$ of adults ride the bus to work in Los Angeles. f. The mean number of cars a person owns in her lifetime is not more than ten. g. About half of Americans prefer to live away from cities, given the choice. h. Europeans have a mean paid vacation each year of six weeks. i. The chance of developing breast cancer is under $11 \%$ for women. j. Private universities' mean tuition cost is more than $\$ 20,000$ per year.

Null and Alternative Hypotheses
Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.
State the null hypothesis, $H_{0}$, and the alternative hypothesis. $H_{a}$, in terms of the appropriate parameter $(\mu \text { or } p)$.
a. The mean number of years Americans work before retiring is 34.
b. At most $60 \%$ of Americans vote in presidential elections.
c. The mean starting salary for San Jose State University graduates is at least $\$ 100,000$ per year.
d. Twenty-nine percent of high school seniors get drunk each month.
e. Fewer than $5 \%$ of adults ride the bus to work in Los Angeles.
f. The mean number of cars a person owns in her lifetime is not more than ten.
g. About half of Americans prefer to live away from cities, given the choice.
h. Europeans have a mean paid vacation each year of six weeks.
i. The chance of developing breast cancer is under $11 \%$ for women.
j. Private universities' mean tuition cost is more than $\$ 20,000$ per year.

Key Concepts

Alternative Hypothesis

The alternative hypothesis (H?) is the assertion that contradicts the null hypothesis. It represents a claim that there is an effect, difference, or deviation from the value specified in the null hypothesis. Depending on the context, it can be directional (one-tailed) or non-directional (two-tailed), indicating whether the parameter is greater than, less than, or simply not equal to the stated value.

One-Tailed and Two-Tailed Tests

In hypothesis testing, the nature of the alternative hypothesis determines whether a one-tailed or two-tailed test is appropriate. A one-tailed test is used when the alternative hypothesis states that the population parameter is either greater than or less than the value specified in the null hypothesis. A two-tailed test is used when the alternative hypothesis simply states that the parameter is different from the null value, without specifying a direction.

Null Hypothesis

The null hypothesis (H?) is a statement asserting that there is no effect or no difference in the parameter of interest. It typically represents a position of equality or a specific benchmark value for a population parameter, such as stating that a mean is equal to a given number or that a proportion is equal to a stated percentage. It is the default assumption that any observed effect is due to chance unless sufficient evidence is presented to reject it.

Parameter

A parameter is a numerical summary that describes a characteristic of a population, such as the mean (?) for quantitative measurements or the proportion (p) for categorical outcomes. In the context of hypothesis testing, parameters are what we use to translate real-world claims or statements into formal statistical hypotheses.

Transcript

Please give Ace some feedback