# Statistics

**PROBLEM 1**

Kathleen Vohs of the University of Minnesota and her coworkers carried out several randomized comparative experiments on the effects of thinking about money. Here’s part of one such experiment. Ask student subject to unscramble 30 sets of five words to make a meaningful phrase from four of the five words. The control group unscrambled phrases like “cold it desk outside is” into “it is cold outside.” The treatment group unscrambled phrases that lead to thinking about money, turning “high salary desk paying” into “a high-paying salary.” Then each subject worked a hard puzzle, knowing that they could ask for help. Here are the times in seconds until subjects asked for help:

Treatment group:

609 444 242 198 174 55 251 466 443

531 135 241 476 482 362 69 160

Control group:

118 272 412 290 140 104 55 189 126

400 91 63 87 142 141 373 156

The researcher suspected that money is connected with self-sufficiency, so that the treatment group would ask for help less quickly on the average. Do the data support this idea? Use a 5% level of significance.

**EXPECTATIONS**

- Draw graphs and charts when appropriate and necessary to demonstrate your reasoning! Label all graphs and charts!

- Display formulas. Write complete sentences to summarize your conclusions.

- If use any table values, clearly state which tables you used (e.g. Table A-2, etc.).

-Attach excel output when appropriate or necessary (e.g. a scatterplot, etc.)**HYPOTHESIS TESTING QUESTIONS**

Your work for all statistical hypothesis testing questions should include the following:

1. Established Ho and Ha.

2. Summary statistics (either computed or given in the problem)

3. The name of the test (e.g. 2sampleTtest or T-test about correlation, etc.)

4. A formula to compute a test statistic (e.g. 1Prop-Z test statistic, etc.)

5. A p-value of the test and/or a critical value from a statistical table.

6. Clearly state the decision rule you use the reach a conclusion. (You may have to sketch a graph to show rejection regions.) Do you “Reject Ho” or do you “Fail to Reject Ho”?

7. State your conclusion in plain language. Use complete sentences.

**Answers 1**

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PROBLEM 2

A company hopes to improve customer satisfaction, setting as a goal “less than 5% negative comments”. A random survey of 350 customers found only 10 with complaints. Does this provide …Loaded dice? You might be suspecting that you have a loaded die. To test this assumption, you roll the die 300 times and observe the frequency of occurrence of each of the faces:

Face …

PROBLEM 4

Classified ads in the Ithaca Journal offered several used Toyota Corollas for sale. Listed

below are the ages of the cars and the advertised prices.

Age (yr) Price Advertised ($)

1 …