Question

5. Which is most likely a curvilinear relationship?

a. IQ and interest in mass market novels sold in grocery stores

b. drunkenness and fine motor skills

c. miles driven and fuel burned

d. minutes spent on phone and size of phone bill

Various Math Problems

6. A social scientist in Austin sees 470 people waiting in line for breakfast tacos at Jo’s on South Congress Ave. Strolling along the sidewalk with her clipboard, she asks each of them two questions. First, “Do you consider yourself more liberal or more conservative?” Second, “Neighborhood gentrification occurs when more affluent people move in to poorer neighborhoods, bringing fancy shops and restaurants and higher real estate prices. Do you think gentrification is mostly good urban revitalization or mostly bad long time resident displacement?”

revitalization displacement

conservative 141 39

liberal 47 243

A. State appropriate null and alternative hypotheses. (6 points)

B. What is the critical value at the .01 level of significance? (4 points)

C. Calculate the test statistic. Keep things tidy and label steps clearly so that your grader can figure out what you’re doing. (10 points)

D. Give a proper English statement of your conclusion and what your conclusion means in terms of error(s) risked and hypotheses rejected or not. Make reference to the particulars of this problem (political orientation, views of gentrification). (10 points)

7. You are studying a cholera outbreak in one part of Mali. Some villages have been hit harder by the outbreak than others. Moreover, some villages have more homes with indoor flush toilets, which reduce people’s exposure to human waste that can spread cholera. With data from just four villages, can you show the relationship between cholera rates and flush toilets to be statistically significant?

village : 1, 2, 3, 4

percentage of homes with flush toilets : 15, 20, 5, 80

cases of cholera per 1000 residents: 9, 4, 12, 2

A. State appropriate null and alternative hypotheses. (6 points)

B. Caldwell’s table of critical values doesn’t go down to 2 df, so I’ll give it to you. The critical value at the .05 level of significance is |0.95|. But you tell me: is it positive or negative here? (4 points)

C. Make a scatterplot for these data. Pay attention to which variable is X and which is Y. (5 points)

D. Calculate the test statistic. Pay attention to which variable is X and which is Y. Keep things tidy and label steps clearly so that your grader can figure out what you’re doing. (10 points)

E. Give a proper English statement of your conclusion and what your conclusion means in terms of error(s) risked and hypotheses rejected or not. Make reference to the particulars of this problem (flush toilets, cholera rates). (10 points)

F. Calculate and interpret the coefficient of determination. (5 points)

8. Recent years of sales data show that 70% of the variance in prices for condos sold in one 40 story building in downtown Austin was determined by the floor on which each condo was located (higher up condos sold for more). Like so:

average sale price (Y bar): $730,000

standard deviation (sY): $40,000

average floor of sold apartments (X bar): 20

standard deviation (sX): 6.9

Estimate the price for a condo on the 38th floor of this building. Keep things tidy and label steps clearly so that your grader can figure out what you’re doing. (10 points) (Hint: don’t get tripped up by the 70% figure – does it represent r or r2 ?)

Answer 1

Solution :

5.

Option (b) is correct.

Drunkenness and fine motor skills has a curvilinear relationship.

Explaination :

Initally its effect is slow but increases very fast due to increase in Alchol. Most likely it shows exponential relationship curvilinear.

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