Suggested languages for you:

Americas

Europe

Q.1

Expert-verifiedFound in: Page 594

Book edition
4th

Author(s)
David Moore,Daren Starnes,Dan Yates

Pages
809 pages

ISBN
9781319113339

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 $\overline{)X}=63.1$ 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.

(a) ${H}_{0}:\mu =64.2$

${H}_{\alpha}\ne 64.2$

(b) ${H}_{0}:P=0.75$

${H}_{\alpha}:P<0.75$

Given in the question that,

Population mean$\left(\mu \right)=64.2$

Sample mean$\left(\overline{)x}\right)=63.1$

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

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

${H}_{0}:\mu =64.2$

${H}_{\alpha}:\mu \ne 64.2$

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:

${H}_{\alpha}:P=0.75$

${H}_{\alpha}:P<0.75$

94% of StudySmarter users get better grades.

Sign up for free