Question

For the study of Jordanian children in Exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.

(a) Calculate the test statistic.

(b) Find the P-value using Table B. Then obtain a more precise P-value from your calculator.

Short answer

a. the test statistic is$-3.094$

b. the P-value using Table B $0.016$

Step-by-step solution

Introduction

A p-value estimates the probability of obtaining the noticed outcomes, it is consistent with expectations that the invalid hypothesis. The lower the p-esteem, the more prominent the statistical significance of the noticed difference

Explanation Part (a)

The sample mean is $\stackrel{-}{x}=11.3$

The sample size is n = $50$

Standard deviation is $1.6$

Using,

localid="1652954330667" $t=\frac{\stackrel{-}{x}-\mu }{\frac{s}{\sqrt{n}}}$

localid="1663929363504" $$\begin{gathered} =\frac{11.3-12}{\frac{1.6}{\sqrt{50}}} \\ =-3.094 \end{gathered}$$

Hence the test statistic islocalid="1663929380848" $-3.094$

Explanation Part (b)

Calculating the degree of freedom,

$n-1=50-1=49$

The p-value is,

$$\begin{gathered} =P\left(t_c>|-3.094|\right) \\ \mathit{=}\mathit{0}\mathit{.}\mathit{0016} \end{gathered}$$

Hence the P-value is$0.0016$