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Edexcel AS Maths Statistical hypothesis testing 1 Section 2: More about hypothesis tests QUESTION AND ANSWERS/SOLUTIONS

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Edexcel AS Maths Statistical hypothesis testing 1 Section 2: More about hypothesis tests QUESTION AND ANSWERS/SOLUTIONS I suspect that a particular coin I have is biased towards heads. In order to investigate this, I toss it 15 times. If X is the number of heads in the 15 tosses, what is the critical region for the hypothesis test conducted at the 5% significance level? (a) X  12 (b) X  12 (c) X  11 (d) X  11 2. I suspect that a particular coin I have is biased. In order to investigate this, I toss it 15 times. If X is the number of heads in the 15 tosses, what is the critical region for the hypothesis test conducted at the 5% significance level? (a) X  3 (b) X  3 or X  12 (c) X  12 (d) 3 < X < 12 3. A pharmaceutical company claims that its new vaccine is 90% effective. To find out if this claim is too high, a hypothesis test is conducted at the 1% significance level with a sample of 14 patients. Using X to denote the number of patients for whom the vaccine is effective, what is the critical value of X? 4. It is claimed that a coin is fair. In order to test this claim it is tossed 18 times. If X is the number of heads in the 18 tosses, what is the acceptance region for the hypothesis test conducted at the 10% significance level? 5. I suspect that my opponent in a card game may be cheating. To test this, I decided to record the suit of the first card dealt after my opponent had shuffled the pack of cards, and to carry out a hypothesis test to see if the probability that a club was dealt first is different from 0.25. I found that on only one of 20 occasions was the first card dealt a club. At which of the significance levels: 10%, 5%, 2 1 2 % and 1%, can I claim that my opponent was cheating? 6. It is claimed that 10% of men can distinguish between butter and margarine, but some people feel that this percentage is too low. Let X be the number of men who can distinguish between butter and margarine. Working at the 5% significance level with a sample of size 12, what is the critical region? A seed manufacturer claims that in a particular variety that he sells there will be one white flower for every three pink flowers. You decide to carry out a hypothesis test to see if this claim is correct, by buying a packet and planting the contents. If p is the probability of a white flower, what is the null hypothesis, H0, which you would use in a hypothesis test? If p is the probability of a white flower, what is the alternative hypothesis, H1, which you would use in a hypothesis test? From the packet you bought, you get 10 white and 10 pink flowers. Which of the statements below are correct? (i) At the 5% significance level, H0 is rejected. (ii) At the 2.5% significance level, H0 is rejected. What is the critical region for this hypothesis test, conducted at the 10% significance level?

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