Question

I am trying to conduct a statistical test on some values I have (maybe a Z or T test), but am confused on what to do. Is there any test I can do if I know:

Test 1: n=43, mean=53.52 s, standard deviation=55.96

Test 2: n=64, mean=52.81 s, standard deviation=47.75

I'm not sure if this is enough info to conduct a test

(For reference, this is representing the average time spent at a birdfeeder in two different locations over 5 hours)

Answer 1

This is more than enough info to run a test. You just need to decide on a level of significance and decide on your hypothesis and you can perform a t-test for difference of means (since the sample standard deviation is used, we will use a t-test. If population standard deviation was known we would have used a z test)

Here is the test in action:

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

​

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=105. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

Hence, it is found that the critical value for this two-tailed test is tc​=1.983, for α=0.05 and df=105.

The rejection region for this two-tailed test is R={t:∣t∣>1.983}.

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=0.07≤tc​=1.983, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.9441, and since p=0.9441≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

Graphically

Please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!