the answer is C… I am having trouble understanding why the probability of type 1 error being 5 percent doesnt mean the same thing as the 95 percent probability of test statistic being between the critical values for a 2 tailed test… would really appreciate if you guys could explain it a bit to help me wrap my head around it… (sorry to offend ppl if it seems like a silly question… i am a noob)
A type I error is when you reject a true null hypothesis. Alpha is that probability (in this case 5%).
If you have a 95% confidence interval and a two-tailed test, you know the critical values will be +/- 1.96 (0.025 in each tail). You can test, for example, the value of 10 (whatever units). Given the same sample size, no matter how many times you calculate the test statistic, it will either be in the rejection region or not. So, the test statistic does not have a probability.
What the 95% confidence interval says is: "I am 95% confident that the observation will fall between +/- 1.96 standard deviations away from the mean.
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