Allied MAT130 final exam

1. Provide an appropriate response.

A teacher was interested in knowing how much tax people pay in the United States. She selected a simple random sample of her friends and asked them about their taxes. Is this sample likely to be representative of all adults in the United States?

2. Form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or make subjective judgments about the results.

A manufacturer of laptop computers claims that only 1% of their computers are defective. In a sample of 600 computers, it was found that 3% were defective. If the proportion of defectives were really only 1%, there would be less than 1 chance in 1000 of getting such a large proportion of defective laptops in the sample. Is there statistically significant evidence against the manufacturer’s claim? Why or why not?

3. Use critical thinking to address the key issue.

A researcher published this survey result: “74% of people would be willing to spend 10 percent more for energy from a non-polluting source”. The survey question was announced on a national radio show and 1,200 listeners responded by calling in. What is wrong with this survey?

4. Provide an appropriate response.

An advertisement for a heating pad says that is can reduce back pain by 200%. What is wrong with this statement?

5. Provide an appropriate response.

Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn’t possible. He said that the expected value was the most likely value in a single roll of the die, and since it wasn’t possible for a die to turn up with a value of 3.5, the expected value couldn’t possibly be 3.5. Who is right? Explain.

6. Provide an appropriate response.

Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

7. Provide an appropriate response.

A poll of 1700 randomly selected students in grades 6 through 8 was conducted and found that 53% enjoy playing sports. Is the 53% result a statistic or a parameter? Explain.

8. Provide an appropriate response.

Define P-values. Explain the two methods of interpreting P-values.

9. Solve the problem. What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether then event is likely.

Claim: An employee of a company is equally likely to take a sick day on any day of the week. Last year, the total number of sick days taken by all the employees of the company was 143. Of these, 52 were Mondays, 14 were Tuesdays, 17 were Wednesdays, 17 were Thursdays, and 43 were Fridays.

10. Provide an appropriate response.

Define independent and dependent samples and give an example of each.

Independent samples are samples where one observation does not affect the outcome of another observation. One example is a sample of the weights of individuals selected at random. We can assume that one person’s weight does not affect any other person’s weight.

11. Describe the error in the stated conclusion.

Given: There is no significant linear correlation between scores on a math test and scores on a verbal test. Conclusion: There is no relationship between scores on the math test and scores on the verbal test.

12. Provide an appropriate response.

List the advantages and disadvantages of nonparametric tests.

13. Provide an appropriate response.

Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

14. Provide an appropriate response.

Describe the Wilcoxon rank-sum test. What type of hypotheses is it used to test? What assumptions are made for this test? What is the underlying concept?

15. Provide an appropriate response.

Describe a run chart and give an example. Refer to the values on each of the axes as you describe the run chart.