Researchers are interested in the mean age of a certain population. A random sample of 10 individuals drawn from the population has a mean of 27. Assuming that the population is approximately normally distributed with variance 20, can we conclude that the mean is different from 30 years? The significance level $\alpha = 0.05$. The p-value is given as 0.0340. The question asks how we can use the p-value in making a decision.

1. Problem Description

Researchers are interested in the mean age of a certain population. A random sample of 10 individuals drawn from the population has a mean of

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7. Assuming that the population is approximately normally distributed with variance 20, can we conclude that the mean is different from 30 years? The significance level $\alpha = 0.05$. The p-value is given as 0.

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0. The question asks how we can use the p-value in making a decision.

2. Solution Steps

The problem describes a hypothesis test to determine if the population mean is different from 30 years. We have a sample mean, sample size, and population variance. The null and alternative hypotheses are:

$H_0: \mu = 30$

$H_1: \mu \neq 30$

The significance level is $\alpha = 0.05$.

The p-value is given as $p = 0.0340$.

In hypothesis testing, we compare the p-value to the significance level $\alpha$. If the p-value is less than or equal to $\alpha$, we reject the null hypothesis. If the p-value is greater than $\alpha$, we fail to reject the null hypothesis.

In this case, we compare $p = 0.0340$ to $\alpha = 0.05$.

Since $0.0340 \leq 0.05$, we reject the null hypothesis $H_0$.

This means that there is sufficient evidence to conclude that the population mean is different from 30 years.

3. Final Answer

Since the p-value (0.0340) is less than the significance level (0.05), we reject the null hypothesis. We conclude that the population mean is different from 30 years.