Now that we have the required sample parameters, we need to compute the test statistic for this given sample. For this, we need the sampling distribution’s standard deviation as well.

Let’s say you’re also given the **population variance as 0.24 **(If you want to know how the population variance is calculated, check the explanation given at the end of the page).

Now let’s go ahead and compute the sampling distribution’s standard deviation

Note that in the above video,** you’re already given the population variance of 0.24.** From this and the given sample size, you need to compute the sampling distribution standard deviation.

Recall, from the Central Limit Theorem, the formula for Sample Distribution’s standard deviation comes out to be σ√n where σ is the population standard deviation and n is the sample size.

Now, given that σ2=0.24 and n=7400. Thus the sampling distribution’s standard deviation is computed as

σ√n=√0.247400=0.00569≈0.006

Thus as you calculated, the sampling distribution’s standard deviation, given from Central Limit Theorem comes out to be **0.006**

Now let’s go ahead and calculate the test statistic for this sample, which you know will be its Z-score.

As, you know, the Z-score can be calculated by the following formula X−μσ/√n . Now for the given problem, we have the parameters as follows

Sample mean(X)=0.39

Population Mean(μ)=0.40

Sampling Distribution Standard Deviation(σ√n)=0.005695≈0.006

Substituting the values, we get Zs=0.39−0.400.005695=−0.010.005695=−1.756. This is the test statistic for our sample data.

In the upcoming segment, you’ll be taking a look at another parameter that’ll help you to find the critical region using this test statistic and finally enable you to make the decision.