Chapter 9: Q.1 (page 594)

Stating hypotheses State the appropriate null and alternative hypotheses in each of the following cases.
(a) The average height of $18$ -year-old American women is $64.2$ inches. You wonder whether the mean height of this year's female graduates from a large local high school (over $3000$ students) differs from the national average. You measure an SRS of $48$ female graduates and find that $X = 63.1$ inches.
(b) Mr. Starnes believes that less than $75 %$ of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of students at the school to help Mr. Starnes test his claim.
- Check conditions for carrying out a test about a population proportion or mean.
- Interpret $P$ -values in context.

Expert verified

(a) $H_{0} : μ = 64.2$

$H_{α} \neq 64.2$

(b) $H_{0} : P = 0.75$

$H_{α} : P < 0.75$

Step by step solution

Given in the question that,

Population mean $(μ) = 64.2$

Sample mean $(x) = 63.1$

Sample size $(n) = 48$ we have to find an SRS of $48$ female graduates and find that $\bar{X} = 63.1$ inches.

Consider $μ$ be the average height of $18$ year old american women. using the information, the null and alternative hypothesis are:

$H_{0} : μ = 64.2$

$H_{α} : μ \neq 64.2$

Given in the question that, population proportion $= 0.75$

Here, $p$ be the population proportion of the students that completed their homework last night.

Using the information, the null and alternative hypotheses are:

$H_{α} : P = 0.75$

$H_{α} : P < 0.75$

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