Factors IndicatIng Nonparametric Inference

1. Explain some factors that might indicate that nonparametric inference might be necessary.
Use the following information to answer questions (2) and (3). Suppose the manager of a large appliance and electronics store wants to estimate the amount spent by customers during the holiday season. He took a random sample of customers and recorded the amount they spent. A histogram of the data shows that the data is strongly left-skewed. The figures below show the confidence intervals for the mean amount spent using (A) raw (untransformed) data, and (B) log-transformed data, which showed a more normally distributed data set.
 
2. Calculate the width of both intervals (note that you will need to convert the log-transformed interval back into dollars) and state which interval is narrower?
3. Which interval should the manager report to the store owner about the typical amount of money spent during the holiday season? Explain.
4. Calculate the mean, median, and geometric mean for the following numbers: 110, 500, 1700, and 31,000. List from smallest to largest and round to the nearest tenth. Show the work!
Suppose the Nielson Organization conducted a survey to find out how many minutes of crime dramas that people watched in one week. Assume that all conditions for the Mann-Whitney test have been met. Use the following test output to answer the questions (5) and (6).
5. State the null and alternative hypothesis to test the claim that adults between the ages of 24 and 39 and adults between the ages of 40 and 55 watch different amounts of crime dramas on television.
6. Using a significance level of 5%, state the correct decision regarding the null hypothesis and write a sentence which summarizes the conclusion and addresses the claim.
Use the following information to answer questions (7) – (10). Can dogs change your level of anxiety in the classroom? Fifty subjects who reported anxiety about attending math class were measured for stress at the beginning of a math class then spent 15 minutes interacting with a dog followed by a forty-five minute math lecture. Each subject was then measured for stress at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
 
7. State the null and alternative hypothesis to test the claim that dogs can affect anxiety levels.
8. Calculate the value of the test statistic and state the value of the p-value?
9. Explain how the binomial model is used to calculate the p-value. Copy and paste statistical output showing this p-value calculated from the binomial distribution.
10. Using a significance level of 5%, state the correct decision regarding the null hypothesis and write a sentence which summarizes the conclusion and addresses the claim