Question

Anemia 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.$t=-3.0936$

b.$p-value=1.638$; using calculator,p-value ≈ 0.998352

Step-by-step solution

Given information

Anemia 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.

Explanation (part a)

Hypothesised mean$\mu ₀=12$

Sample mean$\mathrm{x̄}=11.3$

Sample standard deviation$s=1.6$

Sample size$n=50$

t-score

$t=\frac{\overline{x}-{\mu }_0}{s}\cdot \sqrt{n}$

On plugging all the values, we get$t=-3.0936$

Explanation (part b)

Using Table $B$, the p-value is found to be $p-value=1.638$

Using calculator, the p-value can be find by,

t-score: the test statistic follows the t-distribution with $49$degrees of freedom.

$p-value\approx 0.998352$

Your result is not statistically significant: there is not enough evidence to reject the null hypothesis.

This decision is made at significance level$\alpha =0.05.$