Question

A 95% confidence interval for a population mean is (28, 35).

a) Can you reject the null hypothesis that µ= 34 at the 5% significance level? Why?
b) Can you reject the null hypothesis that µ= 36 at the 5% significance level? Why?

Answer 1

@jim_thompson5910

Answer 2

if \(\mu\) is in the interval you do not reject

if it is not then you reject

Answer 3

Sorry I am still confused... what do you mean?

Answer 4

based on what @Zarkon wrote, we see that in part (a) that µ= 34 is in the interval (28, 35)

since 34 is between 28 and 35

so in part (a) we will not reject the null, in effect, this is accepting the null hypothesis to be true

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In part (b), the mean is now 36 which is NOT in the interval given, so we have to reject the null. The confidence interval is not correct for this mean value

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the idea is that the confidence interval says "the mean is somewhere between the endpoints, 28 and 35". If the mean is really between the endpoints, then you can't reject the null because the statement holds up to be true

If the mean is NOT between the endpoints, then you have to reject the null. The null leads to the mean being between 28 and 35, but the mean is not between those two values

Answer 5

OHH okay! Got it! :)

Thank You! :)

@jim_thompson5910

Answer 6

Here's another example using geography

Let's say we have a town in the US where it produces a special material. We don't know where it is. It could be anywhere in the US.

Someone makes the claim that "the town is between LA and St Louis". If the town is really between those two towns, then the claim is correct and we "accept the null" so to speak. If the town is not between those other two towns, then we have to reject the null and find another claim to support

Answer 7

I'm glad it's making more sense now