Is this stats answer wrong?

A random sample of 10 observations is taken from a normal distribution with unknown mean ų and unknown variance. The sample mean is calculated to be 19.78 and the sample variance is calculated to be 0.811. Test at the 5% level of significance the claim that u < 20.

My answer booklet says to reject H0 for H1, and I have no idea why.

Could someone please help? it would be much appreciated.

Sounds like a t-test, but even without working out the numbers exactly, the difference in the means, 0.22, seems relatively small compared to the std dev/variance. What did you do?

I did z= (19.78-20)/(0.9/sqrt(10)) then I got like -0.77 which is no where near the critical value for 0.05 (it’s like -1.83)

Your numbers sound about right for the student t distribution, but not in terms of making sense of the question.

From a quick google
https://www.thestudentroom.co.uk/showthread.php?t=5257620&p=76736420&page=2#post76736420
n should be 100 which would make the t-distribution pretty much a normal test and that would make the std dev more in line with the mean ~ 2 std dev youd expect for a 95% confidence test.

Oh, thank you!! So it was a misprint. That makes sense, as I know when using sample variance n has to be greater than 30.

The numbers/approach makes sense if n=100, so just work it through with that.

n=10 is too small/info uncertain to say anything really.