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I have got questions regarding Alternative and Null Hypotheses, but it confuses me, and well I just need help as I keep getting stuck on two questions, both about hypothesis but I'm only here to ask about one. The question alters a little each attempt varying between mean and probability, like the following:

  1. The alternative hypothesis is that the mean is different than 45, if the sampling error is 12(Sampling error is the standard error times the z-score), and the sample mean is 59, do we:

  2. The alternative hypothesis is that the mean is greater than 10, if the sampling error is 3, and the sample mean is 12, do we:

  3. The alternative hypothesis is that the mean is less than 5, if the sampling error is 2, and the sample mean is 8, do we:

  4. The alternative hypothesis is that the proportion is different than 60%, if the sampling error is 18%, and the sample proportion is 76%, do we:

    • Reject the null
    • Accept the null
    • Cannot reject the null

I believe a null hypothesis can not be accepted so that should be out of the equation, but i still do not know how to work it out.

Can someone explain to me how to work questions like this out and the explanations?

Many Thanks to all, J

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    $\begingroup$ What is sampling error? $\endgroup$ – user158565 Dec 9 '18 at 16:59
  • $\begingroup$ Sampling error it says it is the standard error times the z-score. We was told it is our range for errors, so for example if our proportion is 70% and sampling error is 10%, it would result in a proportion range of 60 - 80% to account for any errors that could have occurred. $\endgroup$ – user229697 Dec 9 '18 at 17:30
  • $\begingroup$ For the first question, null hypothesis is mean = 45. the range is 47-61, which does not include 45, so null hypothesis should be rejected. Right? $\endgroup$ – user158565 Dec 9 '18 at 17:34
  • $\begingroup$ I believe so, but not sure. The only one i know is Q4, that is cannot reject, but that is because the teacher told us :P. I think it is because 76% falls within the range? If it really is that easy, then i probably did not need to ask the question on here and should have asked the harder one. $\endgroup$ – user229697 Dec 9 '18 at 17:39
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If the null value is not contained within the 95% confidence interval (which is the test score times the standard error, which your exercise has called the sampling error), we are 95% confident that the true parameter is not the null value that the null hypothesis claims, so we reject it. Conversely, if the null is contained within the 95% confidence interval, then the null is one of the values that is consistent with the observed data, so the null hypothesis cannot be rejected.

Anyway,

1/ NULL:mu=45. Alternative: mu$\ne$45. Your observed sample mean is 59, the confidence interval is 12. 59+12=71 and 59-12=47, that range from 71 to 47 doesn't contain the null claimed value, reject the null hypothesis. Evidence supports the alternative hypothesis.

2/NULL:mu=<10. Alternative: mu>10. Your observed sample mean is 12, the confidence interval is 3. 12+3=15 and 12-3=9, that range does contain the null claimed values. Do not have enough evidence to reject the null hypothesis.

3/you can do that one :)

4/NULL:p=60. Alternative: p$\ne$60. Your observed sample mean is 76, the confidence interval is 18. 76+18=94 and 76-18=58, that range 94 to 58, does contain the null claimed values. Do not have enough evidence to reject the null hypothesis.

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  • $\begingroup$ Thanksss. I understand, i think. Would Q3 be that we cannot reject the null, as the Null is =>5, and the range is 6-8 which is more than 5? $\endgroup$ – user229697 Dec 9 '18 at 18:43
  • $\begingroup$ Yeah pretty much. Just that the confidence interval is 8(+-)2 so it's 6 to 10. $\endgroup$ – Huy Pham Dec 9 '18 at 18:53
  • $\begingroup$ Oops, yeah sorry, 6-10. So even though 5 is not included, we cannot reject it due to the fact the Null states it can be = to, or > 5? $\endgroup$ – user229697 Dec 9 '18 at 18:57
  • $\begingroup$ In this case yeah. The way it's worded yes the null is 5 and above. Just a note In case you haven't learnt calculating test statistics yet; In real life, you normally want to hypothesis test the difference between things so the vast majority of null hypotheses is something like mu1=mu2 which is equivalent to mu1-mu2=0. Normally you take means and subtract them from each other and plug that into a significance test e.g. t test which will have some associated p value which takes care of the rejection decision for you. $\endgroup$ – Huy Pham Dec 9 '18 at 19:18
  • $\begingroup$ Understood now, great. Will help me out on my online quiz :), just got one more statistics question to ask but i should probably ask on a new thread. and i see. We have not really done much around null hypothesis and whether to reject or not reject. Luckily i am a business student so after my maths and statistics combined exam in January, no more of it for 4 years. $\endgroup$ – user229697 Dec 9 '18 at 19:22

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