Answer to Question #137098 in Economics for Joe Seri

Question

The amount of Mangoes that are produced each year by a farmer in Waka Village is normally
distributed. The standard deviation of the bags of mangoes is identified as 0.04 grams.
Mangoes that too small and unripe are not bagged. Using your knowledge of hypothesis testing
and a 95% confidence level, execute a two – tailed to prove the claim that μ = 0.50 grams. The
sample mean is 0.51 grams and the sample size is 25 bags of mangoes.

Answer 1

The provided sample mean is $\bar{x}=0.51$ and the known population standard deviation is $\sigma=0.04,$ and the sample size is $n=25.$

The following null and alternative hypotheses need to be tested:

$H_0:\mu=0.50$

$H_1:\mu\not=0.50$

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is $\alpha=0.05,$ and the critical value for a two-tailed test is  $z_c=1.96.$

The rejection region for this two-tailed test is $R=\{z:|z|>1.96\}$  

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu_0}{\sigma/\sqrt{n}}=\dfrac{0.51-0.50}{0.04/\sqrt{25}}=1.25$$

Since it is observed that $|z|=1.25<1.96=z_c,$ it is then concluded that the null hypothesis is not rejected. Therefore, there is not enough evidence to claim that the population mean $\mu$ is different than 0.50, at the 0.05 significance level.

Using the P-value approach: The p-value is $p=0.2113,$ and since $p=0.2113\geq0.05,$ it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean $\mu$ is different than 0.50, at the 0.05 significance level.