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Q.1

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Found in: Page 594

### The Practice of Statistics for AP

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

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

See the step by step solution

## Part (a)Step 1 :Given information

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.

## Part (a) Step2 :Explanation

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

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

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

## Part (b) Step 1:Given Information

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

## Part (b) Step 2:Explanation

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

Using the information, the null and alternative hypotheses are:

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

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