1. A certain tobacco company advertised that its cigarettes contain at most 40 mg of nicotine, but a researcher doubts this claim. The researcher tests 10 randomly selected cigarettes and found the nicotine levels given below.
Test, at a 0.01 significance level, to see whether there is significant evidence that the cigarettes contain more than 40 mg of nicotine.
2. According to official census figures, 8% of couples living together are not married. A researcher took a random sample of 400 couples and found that 9.5% of them are not married. Test at the 15% significance level if the current percentage of unmarried couples is different from 8%.
3. A soft-drink manufacturer claims that its 12-ounce cans do not contain, on average, more than 30 calories. A random sample of 64 cans of this soft drink, which were checked for calories, contained a mean of 32 calories with a standard deviation of 8 calories. Does the sample information support the alternative hypothesis that the cans contain more than 30 calories? Use a significance level of 5%.
a) Based on your decision, which type of error could the sample data have led you to make? Explain what that means in the context of the question
4. A sample of 800 items produced on a new machine showed that 48 of them are defective. The factory will get rid the machine if the data indicates that the proportion of defective items is significantly more than 5%. At a significance level of 10% does the factory get rid of the machine or not?
5. The American Automobile Association (AAA) claims that 54% of fatal car/truck accidents are caused by driver error. A researcher studies 30 randomly selected accidents and finds that 14 were caused by driver error. At a significance level of , can the AAA claim be refuted?
6. A maker of frozen meals claims that the average caloric content of its meals is 800. A researcher tested an SRS of 12 meals and found that the average number of calories was 873 with a standard deviation of 100. Caloric content varies normally. Is there enough evidence to reject the claim at = 0.02?
b) Based on your decision, which type of error could the sample data have led you to make? Explain what that means in the context of the question.