Question

A test at the 5% significance level, weather the single sample values of 82 comes from a normal population with mean 70 and variance 54.
Explain your answer.

Answer 1

$Let's\;calculate\;a\;z-value,\\given\;\overline{x\;}=70\;and\;\sigma=\sqrt{54}=7.348\\Z=\frac{82-70}{7.348}=1.633\\U\sin g\;calculator\;or\;z-table\;we\;\\can\;calculate\;:\\p(z<-Z\;and\;z>Z)=0.102>0.05\\Since\;p-value\;is\;greater\;than\;our\;\\significance\;level,\;we\;can\;conclude\;\\that\;sample\;value\;82\;comes\;from\;a\;\\normal\;population\;with\;mean\;70\;\\and\;variance\;54.$