Question

A researcher claims that the dropout rate at local universities is more than 15%. Last year, 40 individuals from a random sample of 200 local university students withdrew. Is there enough evidence to reject the researcher’s claim? Use α=0.05.

Answer 1

Answer on Question #82837 – Math – Statistics and Probability

Question

A researcher claims that the dropout rate at local universities is more than 15%. Last year, 40 individuals from a random sample of 200 local university students withdrew. Is there enough evidence to reject the researcher’s claim? Use α=0.05.

Solution

One-tailed binomial test:

$H_0$ - the dropout rate $p < 0.15$

$H_1$ - the dropout rate $p \geq 0.15$ (researcher’s claim)

Find the p-value

$$\begin{aligned} P_{p=0.15} (X \geq 40) &= P_{p=0.15} \left( \frac{X - 200p}{\sqrt{200p(1-p)}} \geq \frac{40 - 200p}{\sqrt{200p(1-p)}} \right) \\ &= P \left( z \geq \frac{40 - 200 \cdot 0.15}{\sqrt{200 \cdot 0.15 \cdot 0.85}} \right) \\ &= 1 - F(1.98) \\ \end{aligned} = 1 - 0.976 = 0.024$$

We used normal approximation of binomial distribution.

Since p-value is less than the critical level $\alpha = 0.05$ we reject the null hypothesis and accept the researcher’s claim.

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