Question

Suppose that a hypothesis test is conducted. 12 out of 100 subjects have the necessary qualities. The null hypothesis is that the proportion of the subjects who have the necessary qualities is equal to 0.2, while the alternative hypothesis is that this proportion is less than 0.2. The p-value is 0.023. Using a 5% significance level, state the conclusion to the hypothesis test in context. A : The p-value is less than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2. B : The p-value is less than the significance level, so we do not reject the null hypothesis. We cannot conclude anything about the proportion of the subjects who have the necessary qualities. C : The p-value is less than the significance level, so we do not reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is equal to 0.2. D : The p-value is more than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2. E : The p-value is more than the significance level, so we do not reject the null hypothesis. We cannot conclude anything about the proportion of the subjects who have the necessary qualities.

Answer 1

Answer: A: The p-value is less than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.

Explanation:

Here, p value = 0.023

significance level = 0.05

As p value < 0.05

Answer 2

Option A

The p-value is less than the significance level of 0.05 chosen and so we reject the null hypothesis H0 and can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.

Explanation:

Normally, in hypothesis testing, the level of statistical significance is often expressed as the so-called p-value. We use p-values to make conclusions in significance testing. More specifically, we compare the p-value to a significance level "α" to make conclusions about our hypotheses.

If the p-value is lower than the significance level we chose, then we reject the null hypotheses H0 in favor of the alternative hypothesis Ha. However, if the p-value is greater than or equal to the significance level, then we fail to reject the null hypothesis H0

though this doesn't mean we accept H0 automatically.

Now, applying this to our question;

The p-value is 0.023 while the significance level is 0.05.

Thus,p-value is less than the significance level of 0.05 chosen and so we reject the null hypothesis H0 and can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.

The only option that is correct is option A.