Hypothesis testing with normal distribution

[resurgance2001]

I have the question and an answer to said question below.

I am only used to hypothesis testing using binomial distributions. Can someone help
me to understand please how the critical value of T is obtained and how one then uses this to decide whether to accept Ho or whether to reject Ho. I am confused because with all the binomial hypothesis tests it is when the value fall within the critical region that we would normal reject Ho because we are saying that under Ho the particular value found is too extreme, too unlikely, too low a probability so we reject Ho. However, with this question it seems to be reversed. Thanks Peter

 

[Harry_the_cat]

If your test statistic lies in the tail of your distribution, then the null hypothesis is rejected. Here it doesn't, so the null hypothesis is not rejected.

 

[resurgance2001]

If your test statistic lies in the tail of your distribution, then the null hypothesis is rejected. Here it doesn't, so the null hypothesis is not rejected.

Thank you. I can see where I was getting confused. My understanding is that the critical region is the tiny bit at the ends of the distibution, the lower the significance level the tinier the the tale(s). However , the way the author, of the answer I was given, has expressed it saying that this test statistic falls within the critical region, but he is talking about the region between the tales and that is what led to the confusion. It’s just the use of terminology. What you have said is very clear. I am guessing that the critical region can be found using tables or the calculator. Thanks!