# University X has 20,000 students. Suppose Irah has drawn a simple random sample of 600 students...

## Question:

University X has 20,000 students. Suppose Irah has drawn a simple random sample of 600 students from University X. In this sample, 240 students at University own Apple iPhones. At a 95% level of confidence, test the null hypothesis that not more than 7500 students at University X own Apple iPhones.

## Confidence Interval

The confidence interval provides the range of value which mean that the value of true population paramter lies within the confidence interval at the given confidence level.

## Answer and Explanation:

**Given information**

Sample size: 600

Number of students at University own Apple iPhones: 240

The value of sample proportion is given below.

{eq}\begin{align*} \hat P &= \dfrac{X}{n}\\ &= \dfrac{{240}}{{600}}\\ &= 0.4 \end{align*}{/eq}

The 95% confidence limit is calculated as follows.

{eq}\begin{align*} P\left( {\hat P - {Z_{\alpha /2}}\sqrt {\dfrac{{\hat P\left( {1 - \hat P} \right)}}{n}} < p < \hat P + {Z_{\alpha /2}}\sqrt {\dfrac{{\hat P\left( {1 - \hat P} \right)}}{n}} } \right) &= 0.95\\ P\left( {0.4 - 1.96\sqrt {\dfrac{{0.4\left( {1 - 0.4} \right)}}{{600}}} < p < 0.4 + 1.96\sqrt {\dfrac{{0.4\left( {1 - 0.4} \right)}}{{600}}} } \right) &= 0.95\\ P\left( {0.3608 < p < 0.4392} \right) &= 0.95 \end{align*}{/eq}

The value of true proportion is (7500/20000 = 0.375) which lies within the interval which mean the null hypothesis is failed to rejected and it is concluded that not more than 7500 students at University X own Apple iPhones.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 3