Q.37 - The Practice of Statistics for AP

Question

Lefties Refer to Exercise 33. In Simon's SRS, 16 of the students were left-handed.

(a) Calculate the test statistic.

(b) Find the P-value using Table A. Show this result as an area under a standard Normal curve,

Step-by-Step Solution

Answer

a.$1.23$

b. $0.218$

Step 1: Introduction

The normal distribution is a consistent likelihood appropriation that is balanced on the two sides of the mean, so the right half of the middle is a perfect representation of the left side. The region under the ordinary dissemination bend addresses likelihood and the absolute region under the bend aggregates to one.

Step 2: Explanation Part (a)

The sample size is n = $100$

The number of left-handed students is x = $16$

Population proportion is p = $12\%=0.12$

sample proportion $\stackrel{-}{p}=\frac{x}{n}=\frac{16}{100}=0.16$

calculating the null and alternative hypotheses,

$\begin{array}{r}{H}_0:p=0.12\\ H_a:p\ne 0.12\end{array}$

Using the formula,

$z=\frac{\stackrel{-}{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}$

$=\frac{0.16-0.12}{\sqrt{\frac{0.12(1-0.12)}{100}}}=1.23$

Step 3: Explanation Part (b)

The p-value is calculated as,

$=2\times P(Z>|Z\left|\right)$

$=2\times P(Z>|1.23\left|\right)$

$=2\times 0.109=0.218$

The standard normal curve is,