## Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

Depending on how you want to "summarize" the exam performances will determine how you might want to write a more specific null and alternative hypothesis. For example, you could compare the **mean** exam performance of each group (i.e., the "seminar" group and the "lectures-only" group). This is what we will demonstrate here, but other options include comparing the **distributions**, **medians**, amongst other things. As such, we can state:

Mickey -UCLA True/FalseTYPE1ERROR TESTING CONCEPT STATISTICST= 2 ComprehensionD= 3 GeneralBack to 1489-1Back to 1490-1

## Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

Thomas watched every forfour weeks. In that time, 30 contestants switched doors, and 18 of them won.

(a) At the 0.05 significance level, is it true or false that yourchance of winning is 2/3 if you switch doors?

(b) At the 95% confidence level, estimate your chance of winningif you switch doors.

(c) If you don’t switch doors, your chance of winning is1/3. Using your answer to (b), is switching doors definitely a goodstrategy, or is there some doubt?

## rejecting the null hypothesis when it is false.

If you keep giving the universe opportunities to send you datathat contradict the null hypothesis, but you keep getting data that areconsistent with the null, then you begin to think that thenull hypothesis *shouldn’t* be rejected, that it’sactually true.

## rejecting the null hypothesis when the alternative is true.

**Example 11:** Suppose your null hypothesis is “the average package containsthe stated net weight,” your alternative is “the averagepackage contains less than the stated net weight,” and yoursignificance level α is 0.05.

## not rejecting the null hypothesis when the alternative is true.

You therefore **fail to reject H _{0}** (and don’tmention H

_{1}).The sample you have could have come about by randomselection if H

_{0}is true, but it could also have come about byrandom selection if H

_{0}is false. In other words, you don’tknow whether H

_{0}is actually true, or it’s false but thesample data just happened to fall not too far from H

_{0}.

## the null hypothesis is rejected when it is true.

If your p-value is greater than your significance level,you have shown that random chance couldaccount for your results if H_{0} is true. You don’t know thatrandom chance is *the* explanation, just that it’s a*possible* explanation. The data are**not statistically significant**.

## the result would be unexpected if the null hypothesis were true.

If your p-value is less than your significance level,you have shown that your sample resultswere unlikely to arise by chance if H_{0} is true. The data are**statistically significant**.You therefore **reject H _{0} and accept H_{1}.**

## The failure to reject does not imply the null hypothesis is true.

The p-value isnt as mysterious as most analysts make it out to be. It is a way of not having to calculate the confidence interval for a t-test but simply determining the confidence level with which null hypothesis can be rejected.