Difference between “at least” and “more than” in hypothesis testing?












0














Question given to me:




A drug to reduce blood pressure is administered to n = 300 patients. After 15 minutes, 276 had blood pressure in the normal range.The company wants to claim that the drug is effective for more than 90% of patients. Using a significance level of $alpha = .05$, determine if they can do this, or if they should make the more conservative claim that the drug is at least 90% effective.




My instructor's "correct" hypotheses:




$campaign 1: H_{0}: widehat{p}= .9, H_{a}: widehat{p}> .9, campaign 2: H_{0}: widehat{p}= .9, H_{a}: widehat{p}< .9$




My main question is in the title; wouldn't "at least" just be inclusive of 90% and since it is continuous, be essentially the same as "more than"?






statistics hypothesis-testing







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  • In general your null hypothesis should have enough information that you can exactly calculate probabilities (so it should exactly specify parameters) while your alternative hypothesis should be disjoint from your null hypothesis. So the inequalities in a proper test should be strict.
    – Ian
    Oct 27 '16 at 18:16










  • That said, there seems to be some disagreement between the symbolic specification of the tests and the text. I have no idea where the "<" came from in the second case. Also, as I said before you can't really have your alternative hypothesis be "the drug is at least 90% effective", it can only be "the drug is more than 90% effective", because it makes no sense for the alternative hypothesis to overlap with the null hypothesis.
    – Ian
    Oct 27 '16 at 18:16










  • I had the same idea, I'll have to check if there is a mistake in the question.
    – Jason
    Oct 27 '16 at 18:34
















0














Question given to me:




A drug to reduce blood pressure is administered to n = 300 patients. After 15 minutes, 276 had blood pressure in the normal range.The company wants to claim that the drug is effective for more than 90% of patients. Using a significance level of $alpha = .05$, determine if they can do this, or if they should make the more conservative claim that the drug is at least 90% effective.




My instructor's "correct" hypotheses:




$campaign 1: H_{0}: widehat{p}= .9, H_{a}: widehat{p}> .9, campaign 2: H_{0}: widehat{p}= .9, H_{a}: widehat{p}< .9$




My main question is in the title; wouldn't "at least" just be inclusive of 90% and since it is continuous, be essentially the same as "more than"?






statistics hypothesis-testing







share|cite|improve this question
























  • In general your null hypothesis should have enough information that you can exactly calculate probabilities (so it should exactly specify parameters) while your alternative hypothesis should be disjoint from your null hypothesis. So the inequalities in a proper test should be strict.
    – Ian
    Oct 27 '16 at 18:16










  • That said, there seems to be some disagreement between the symbolic specification of the tests and the text. I have no idea where the "<" came from in the second case. Also, as I said before you can't really have your alternative hypothesis be "the drug is at least 90% effective", it can only be "the drug is more than 90% effective", because it makes no sense for the alternative hypothesis to overlap with the null hypothesis.
    – Ian
    Oct 27 '16 at 18:16










  • I had the same idea, I'll have to check if there is a mistake in the question.
    – Jason
    Oct 27 '16 at 18:34














0












0








0







Question given to me:




A drug to reduce blood pressure is administered to n = 300 patients. After 15 minutes, 276 had blood pressure in the normal range.The company wants to claim that the drug is effective for more than 90% of patients. Using a significance level of $alpha = .05$, determine if they can do this, or if they should make the more conservative claim that the drug is at least 90% effective.




My instructor's "correct" hypotheses:




$campaign 1: H_{0}: widehat{p}= .9, H_{a}: widehat{p}> .9, campaign 2: H_{0}: widehat{p}= .9, H_{a}: widehat{p}< .9$




My main question is in the title; wouldn't "at least" just be inclusive of 90% and since it is continuous, be essentially the same as "more than"?






statistics hypothesis-testing







share|cite|improve this question















Question given to me:




A drug to reduce blood pressure is administered to n = 300 patients. After 15 minutes, 276 had blood pressure in the normal range.The company wants to claim that the drug is effective for more than 90% of patients. Using a significance level of $alpha = .05$, determine if they can do this, or if they should make the more conservative claim that the drug is at least 90% effective.




My instructor's "correct" hypotheses:




$campaign 1: H_{0}: widehat{p}= .9, H_{a}: widehat{p}> .9, campaign 2: H_{0}: widehat{p}= .9, H_{a}: widehat{p}< .9$




My main question is in the title; wouldn't "at least" just be inclusive of 90% and since it is continuous, be essentially the same as "more than"?






statistics hypothesis-testing




statistics hypothesis-testing






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share|cite|improve this question













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share|cite|improve this question








edited Oct 27 '16 at 18:09

























asked Oct 27 '16 at 17:16









Jason

11




11












  • In general your null hypothesis should have enough information that you can exactly calculate probabilities (so it should exactly specify parameters) while your alternative hypothesis should be disjoint from your null hypothesis. So the inequalities in a proper test should be strict.
    – Ian
    Oct 27 '16 at 18:16










  • That said, there seems to be some disagreement between the symbolic specification of the tests and the text. I have no idea where the "<" came from in the second case. Also, as I said before you can't really have your alternative hypothesis be "the drug is at least 90% effective", it can only be "the drug is more than 90% effective", because it makes no sense for the alternative hypothesis to overlap with the null hypothesis.
    – Ian
    Oct 27 '16 at 18:16










  • I had the same idea, I'll have to check if there is a mistake in the question.
    – Jason
    Oct 27 '16 at 18:34


















  • In general your null hypothesis should have enough information that you can exactly calculate probabilities (so it should exactly specify parameters) while your alternative hypothesis should be disjoint from your null hypothesis. So the inequalities in a proper test should be strict.
    – Ian
    Oct 27 '16 at 18:16










  • That said, there seems to be some disagreement between the symbolic specification of the tests and the text. I have no idea where the "<" came from in the second case. Also, as I said before you can't really have your alternative hypothesis be "the drug is at least 90% effective", it can only be "the drug is more than 90% effective", because it makes no sense for the alternative hypothesis to overlap with the null hypothesis.
    – Ian
    Oct 27 '16 at 18:16










  • I had the same idea, I'll have to check if there is a mistake in the question.
    – Jason
    Oct 27 '16 at 18:34
















In general your null hypothesis should have enough information that you can exactly calculate probabilities (so it should exactly specify parameters) while your alternative hypothesis should be disjoint from your null hypothesis. So the inequalities in a proper test should be strict.
– Ian
Oct 27 '16 at 18:16




In general your null hypothesis should have enough information that you can exactly calculate probabilities (so it should exactly specify parameters) while your alternative hypothesis should be disjoint from your null hypothesis. So the inequalities in a proper test should be strict.
– Ian
Oct 27 '16 at 18:16












That said, there seems to be some disagreement between the symbolic specification of the tests and the text. I have no idea where the "<" came from in the second case. Also, as I said before you can't really have your alternative hypothesis be "the drug is at least 90% effective", it can only be "the drug is more than 90% effective", because it makes no sense for the alternative hypothesis to overlap with the null hypothesis.
– Ian
Oct 27 '16 at 18:16




That said, there seems to be some disagreement between the symbolic specification of the tests and the text. I have no idea where the "<" came from in the second case. Also, as I said before you can't really have your alternative hypothesis be "the drug is at least 90% effective", it can only be "the drug is more than 90% effective", because it makes no sense for the alternative hypothesis to overlap with the null hypothesis.
– Ian
Oct 27 '16 at 18:16












I had the same idea, I'll have to check if there is a mistake in the question.
– Jason
Oct 27 '16 at 18:34




I had the same idea, I'll have to check if there is a mistake in the question.
– Jason
Oct 27 '16 at 18:34










1 Answer
1






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oldest

votes


















0














Yes. I give a calculus-based explanation.



The (Riemann) integral doesn't care if you remove one point. In fact, it doesn't care if you remove countably many points. The integral will still be the same.



Now in these tests you use the normal distribution, a continuous distribution. The area is computed using an integral, approximated by your tables. It doesn't matter if you have the strict inequality or not, the result will still be the same.






share|cite|improve this answer





















  • Thanks @Sean, however, my professor provided $H_{a}: widehat{p}> .9$ for "more than" and $H_{a}: widehat{p}< .9$ for "atleast". This must be a mistake?
    – Jason
    Oct 27 '16 at 18:12










  • Yow, I saw that. I feel like your instructor is wrong but I'm not quite confident. This makes me uneasy.
    – Sean Roberson
    Oct 27 '16 at 18:22











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1 Answer
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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0














Yes. I give a calculus-based explanation.



The (Riemann) integral doesn't care if you remove one point. In fact, it doesn't care if you remove countably many points. The integral will still be the same.



Now in these tests you use the normal distribution, a continuous distribution. The area is computed using an integral, approximated by your tables. It doesn't matter if you have the strict inequality or not, the result will still be the same.






share|cite|improve this answer





















  • Thanks @Sean, however, my professor provided $H_{a}: widehat{p}> .9$ for "more than" and $H_{a}: widehat{p}< .9$ for "atleast". This must be a mistake?
    – Jason
    Oct 27 '16 at 18:12










  • Yow, I saw that. I feel like your instructor is wrong but I'm not quite confident. This makes me uneasy.
    – Sean Roberson
    Oct 27 '16 at 18:22
















0














Yes. I give a calculus-based explanation.



The (Riemann) integral doesn't care if you remove one point. In fact, it doesn't care if you remove countably many points. The integral will still be the same.



Now in these tests you use the normal distribution, a continuous distribution. The area is computed using an integral, approximated by your tables. It doesn't matter if you have the strict inequality or not, the result will still be the same.






share|cite|improve this answer





















  • Thanks @Sean, however, my professor provided $H_{a}: widehat{p}> .9$ for "more than" and $H_{a}: widehat{p}< .9$ for "atleast". This must be a mistake?
    – Jason
    Oct 27 '16 at 18:12










  • Yow, I saw that. I feel like your instructor is wrong but I'm not quite confident. This makes me uneasy.
    – Sean Roberson
    Oct 27 '16 at 18:22














0












0








0






Yes. I give a calculus-based explanation.



The (Riemann) integral doesn't care if you remove one point. In fact, it doesn't care if you remove countably many points. The integral will still be the same.



Now in these tests you use the normal distribution, a continuous distribution. The area is computed using an integral, approximated by your tables. It doesn't matter if you have the strict inequality or not, the result will still be the same.






share|cite|improve this answer












Yes. I give a calculus-based explanation.



The (Riemann) integral doesn't care if you remove one point. In fact, it doesn't care if you remove countably many points. The integral will still be the same.



Now in these tests you use the normal distribution, a continuous distribution. The area is computed using an integral, approximated by your tables. It doesn't matter if you have the strict inequality or not, the result will still be the same.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Oct 27 '16 at 17:21









Sean Roberson

6,38031327




6,38031327












  • Thanks @Sean, however, my professor provided $H_{a}: widehat{p}> .9$ for "more than" and $H_{a}: widehat{p}< .9$ for "atleast". This must be a mistake?
    – Jason
    Oct 27 '16 at 18:12










  • Yow, I saw that. I feel like your instructor is wrong but I'm not quite confident. This makes me uneasy.
    – Sean Roberson
    Oct 27 '16 at 18:22


















  • Thanks @Sean, however, my professor provided $H_{a}: widehat{p}> .9$ for "more than" and $H_{a}: widehat{p}< .9$ for "atleast". This must be a mistake?
    – Jason
    Oct 27 '16 at 18:12










  • Yow, I saw that. I feel like your instructor is wrong but I'm not quite confident. This makes me uneasy.
    – Sean Roberson
    Oct 27 '16 at 18:22
















Thanks @Sean, however, my professor provided $H_{a}: widehat{p}> .9$ for "more than" and $H_{a}: widehat{p}< .9$ for "atleast". This must be a mistake?
– Jason
Oct 27 '16 at 18:12




Thanks @Sean, however, my professor provided $H_{a}: widehat{p}> .9$ for "more than" and $H_{a}: widehat{p}< .9$ for "atleast". This must be a mistake?
– Jason
Oct 27 '16 at 18:12












Yow, I saw that. I feel like your instructor is wrong but I'm not quite confident. This makes me uneasy.
– Sean Roberson
Oct 27 '16 at 18:22




Yow, I saw that. I feel like your instructor is wrong but I'm not quite confident. This makes me uneasy.
– Sean Roberson
Oct 27 '16 at 18:22


















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