State the H_o and H₁, indicate the appropriate test, and if it is one-tailed (directional) or two-tailed (non-directional).

1. A manufacturer claims that each can of mixed nuts he sells contains an average of 10 cashew nuts. A sample of 15 cans of these mixed nuts had an average of 8 cashew nuts with a standard deviation of 0.20. On the basis of these data you'd like to test the manufacturer's claim.

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1. A seat belt manufacturer specifies that his belts will, on the average withstand a 6000 lb. strain before breaking. We test a random sample of 28 seat belts and measure the breaking point of

each.

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1. Two groups of 15 people participated in an experiment on whether "positive thinking" improves learning. People in the first group spent 10 minutes thinking positively and then performed a learning task. People in the second group spent 10 minutes reading dull magazine stories and then did the same learning task. Test the hypothesis that "thinking positively" improves average learning rate.

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1. A top-notch farmer claims that one of the reasons his livestock is bigger and healthier than his neighbour's is that he makes pets out of his livestock whereas his neighbor does not. His neighbor runs an experiment to see if he might be right. He randomly selects two samples of one-week old lambs and weighs each lamb. For one sample, he names the lambs, pets them, and encourages his children to play with them. The others he treats in his usual manner-no names, no petting, no playing. At 140 days of age, he re-weighs each lamb and records the difference between the initial weight and this final weight. How would you determine whether tender, loving care improves weight gain?

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1. The S.M.A.R.T.E.E. aptitude test for western Canadian university students has been standardized so that scores will be normally distributed with m= 100 ands = 17. Using this test to assess intelligence, Professor Dullwit compares a control group of 25 students with an experimental group of 27 students who had been injected with RNA extracted from their professor. You'd like to know if the RNA has any effect on aptitude

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1. Do blondes have more fun? You decide to find out by randomly selecting a group of 35 brunettes. For three months you record the number of dates each has had. Then you have all your subjects dye their hair blonde, and you record the number of dates each has over the next three months. You compare average number of dates per month as brunettes and as blondes to see if blondes have more fun.

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1. Father (insurance agent) and son (16 years old) are arguing. The son claims that teenagers are less likely to be involved in car accidents and the father claims teens have more accidents. The father pulls up some data which shows that in the last month he settled 25 accident claims for his clients age 20 - 40 and that 28 accident claims for his teenage clients. Based on these data what statistical test can they use to settle their argument?

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1. An instructor gives his class an examination that over the past 20 years has had a mean of 53 and a standard deviation of 7 (population). His present class of 22 students obtains a mean of 73 with a standard deviation of 6. How would you determine if the present class is superior to previous classes?

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1. Twenty-two women are sent a "self-confidence questionnaire and an offer to receive a free beauty and fashion makeover. All 22 women accept and show up with their completed self-confidence questionnaire. One week after the makeover, the women are again asked to fill out the "self-confidence" questionnaire. Does the makeover significantly change their self-confidence ratings?

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1. An anthropologist, after many years of research, hypothesizes that women are shorter than men. She knows that the average height of Canadian men is 5'10". She randomly selects a group of 20 women and measure the height of each. Test her hypothesis.

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