Q.14 - The Practice of Statistics for AP

Question

For the study of Jordanian children in Exercise 4, the sample mean hemoglobin level was 11.3 g/dl and the sample standard deviation was 1.6 g/dl. A significance test yields a P-value of 0.0016.

(a) Interpret the P-value in context.

(b) What conclusion would you make if $\alpha$= 0.05? $\alpha$= 0.01? Justify your answer.

Step-by-Step Solution

Answer

a. There is a chance of $0.16\%$of obtaining a sample mean when the mean population is$12$.

b. There is enough evidence against null hypothesis.

Step 1: introduction

Given,

mean population is $11.3$

standard deviation is $1.6$

sample size is $50$

new population value is $0.0016$

Step 2: explanation part (a)

Calculating the null and alternative hypotheses,

population mean value is $12$

$\begin{array}{r}{H}_o:\mu =12\\ H_a:\mu <12\end{array}$

Hence there is a $0.16\%$ chance of obtaining a sample mean of $11.3$ gram per deciliter of blood or more.

Step 3: explanation part (b)

Now,

 Population mean when $\alpha =0.05$

p = $0.0101$ which is less than $0.05$

Thus the null hypothesis is invalid.

 Population mean when $\alpha =0.01$

p = $0.0016$ which is greater than $0.01$

Thus the null hypothesis is invalid as there is enough evidence against the null hypothesis