Some of the following statements refer to the null...

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, Ho, and the 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.

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.
State the null hypothesis, Ho, and the 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

Null Hypothesis

The null hypothesis (H?) is a statement used in statistical tests that asserts no effect or no difference, often representing a status quo or baseline condition. It serves as a default claim that any observed difference in sample data occurs due to random chance rather than a systematic effect, and it is usually expressed in equality form (e.g., equal to a specific value).

Alternative Hypothesis

The alternative hypothesis (H?) is a statement used in hypothesis testing that contradicts the null hypothesis by representing the presence of an effect, difference, or change. It is the claim that the researcher aims to support, often expressed using inequalities or expressions of not equal conditions (e.g., greater than, less than, or not equal to a certain value).

Parameter Notation

Parameter notation involves using symbols such as ? (for means) and p (for proportions) to represent key characteristics of a population. This notation is essential in formulating hypotheses, as it provides a concise and universally understood framework for stating the quantities that are being tested in statistical inference.

One-Tailed vs. Two-Tailed Tests

One-tailed tests focus on an effect in one specific direction (either greater than or less than a given value), while two-tailed tests check for the possibility of an effect in both directions (simply not equal to a specific value). The choice between one-tailed and two-tailed tests affects how the alternative hypothesis is structured and determines the distribution of the critical region during hypothesis testing.

Transcript

00:01 This problem gives us either the null or the alternative hypothesis, and we need to figure out which it is and then figure out the other one using the appropriate parameter.

00:14 So the two options for the parameters are mu, which means mean, or p, which is proportion or percentage.

00:24 Now, the way we figure out if this is a null or an alternative hypothesis is if these two rules, and i think you should have them written down.

00:34 The first one, if we have a scenario involving a less than or equal to or a greater than or equal to, this is usually the null hypothesis, h0.

00:48 And if we have a scenario where it is an equal to and not equal to case, the equal to option is hnol, and the not equal to case is the alternative.

01:01 So we'll do these two rules to solve these problems.

01:07 So the mean years working is exactly 34 .34.

01:14 So that is going to be a null hypothesis.

01:19 So h -null.

01:20 Now, mean means we use the letter mu.

01:25 So mu is equal to 34 .34.

01:29 So that means our alternative is just the alternative.

01:34 What's the alternative? mu is not equal to 34 .34 .4.

01:42 Okay, the next one.

01:44 At most, 60 % of people vote.

01:50 So at most, that sounds like a less than or equal to, which means the case for less than or equal to goes to the null hypothesis.

02:03 So h -null would be that the percentage or proportion of people who vote are at most 60%, or 0 .6.