Significance Hypothesis Testing

Question

Given an assumed mean of 60, a standard deviation of 6, and a population with a sample size of 50 and a population mean of 62.6, I was able to set up two hypotheses,

H0, $\mu=60$

H1, $\mu \ne 60$

I was attempting to solve this problem by a z test, which yields a result of 3.06, how am I able to figure out if this result is significant, so that I can determine whether to accept or reject the null hypothesis?

Answer 1

A Z-score of 3.06 is extremely high, meaning that you are in the extrem right queue...you rejcect the hypothesis for almost any $\alpha$, being your pvalue very very low ($\approx 0.22\%$)

Usually there are two main steps of significance:

• $5\%$, significant

• $1\%$, high significant

Answer 2

That depends on your significance level.

For example, $95\%$ confidence level, the rejection region is $|Z|>1.96$. Since $3.06$ is bigger than $1.96$, we reject the null hypothesis.