A study was conducted to determine whether the standard deviation of monthly maintenance costs of a Pepper aircraft is $300. A sample of 30 such crafts had a mean monthly maintenance cost of $3,025 and standard deviation of $325. By 5% level of significance, are the population and sample variances significantly different or not? What would be null vs. alt. H in this case?

ho: sigma=300 ha: sigma <> 300 (Not equal to)

null and alt are pretty easy. just remember that null always has equality. either = or greater/less then or equal to.

" By 5% level of significance, are the population and sample variances significantly different or not? " Geez… Where did this question come from? Ans: Yes they are different because a) The sample variance is random and the population variance isn’t b) The sample variance is an estimate of the population variance that is equal to it with probability = 0 c) We don’t do hypothesis tests about sample anything.

Well, any question could appear odd… Actually I was try to ask H0 and Ha here. Original Q: A study was conducted to determine whether the standard deviation of monthly maintenance costs of a Pepper aircraft is $300. ho: sigma<> 300 (Not equal to) ha: sigma =300 (Does the study want to prove it is $300?) What if the wording is changed as: A study was conducted to determine whether the standard deviation of monthly maintenance costs of a Pepper aircraft is DIFFERENT FROM $300. ho: sigma=300 ha: sigma <> 300 (Not equal to) Help to clear the confusion? Thx.

i think you’re overthinking this. just remember, null hypothesis always contains a statement of equality.

I see… a good way to get this. Thx, jut111.

hyang Wrote: ------------------------------------------------------- > Well, any question could appear odd… > > Actually I was try to ask H0 and Ha here. > > Original Q: A study was conducted to determine > whether the standard deviation of monthly > maintenance costs of a Pepper aircraft is $300. > ho: sigma<> 300 (Not equal to) > ha: sigma =300 (Does the study want to prove it is > $300?) > This is not a possible test. You will never reject H0. How could you ever conclude beyond a reasonable doubt that sigma = 300? > > What if the wording is changed as: > A study was conducted to determine whether the > standard deviation of monthly maintenance costs of > a Pepper aircraft is DIFFERENT FROM $300. > ho: sigma=300 > ha: sigma <> 300 (Not equal to) > > Help to clear the confusion? Thx.

jut111 Wrote: ------------------------------------------------------- > i think you’re overthinking this. just remember, > null hypothesis always contains a statement of > equality. the above statement is y for one-tail. in the condition of two-tails, H0(null hypothesis) should be the researcher wants to reject.