Q. 68 - The Practice of Statistics for AP

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.

Step-by-Step Solution

Answer

a. $t = -3.0936$

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

Step 1: 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.

Step 2: 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 $t = -3.0936$

Step 3: 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 $\alpha = 0.05.$