Exam 8: Regression, Associations, and Predictive Modeling

Find a 99% confidence interval for the difference in the proportion of Britons and Canadians who read at least one book in the last year. Interpret your interval.

A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads On the next flip is

All airline passengers must pass through security screenings, but some are subjected to additional searches as well. Some travelers who carry laptops wonder if that makes them more likely to be searched. Data for 420 passengers aboard a cross-country flight are summarized in the table shown. Does it appear that being subjected to an additional search is independent of carrying a laptop computer? Explain.

Doctors at a technology research facility randomly assigned equal numbers of people to use computer keyboards in two rooms. In one room a group of people typed a manuscript using standard keyboards, while in the other room people typed the same manuscript using ergonomic keyboards to see if those people could type more words per minute. After collecting data for several days the researchers tested the hypothesis $\mathrm { H } _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ against the one-tail alternative and found $P = 0.22$ . Which is true?

Suppose a school district decides to randomly test high school students for attention deficit Disorder (ADD). There are three high schools in the district, each with grades 9-12. The school Board pools all of the students together and randomly samples 250 students. Is this a simple Random sample?

Personal debt According to The World Almanac and Book of Facts 2004, the debt per capita for the years 1990-2001 gives the following scatterplot: Regression output gives the equation of the regression line as Debt $= - 2,231,226 + 1128$ (Year) with $R ^ { 2 } = 98.8 \%$ . a. What is the response variable? b. What is the correlation coefficient $r$ ? c. Explain in context what the slope of the line means. d. Explain in context what $R ^ { 2 } = 98.8 \%$ means. e. You decide to take a look at a residuals plot before making any predictions. Based on the following residuals plot, does linear regression seem appropriate for these data? Explain.

The boxplots show fuel economy of 2011 model cars for the classes shown. a. Which class offers the car with the best gas mileage, and what is the mileage of that car? b. Which class has the highest median gas mileage, and how much is it? c. Which class of car has the smallest range of fuel economy, and what is it? d. Which class of car has the smallest IQR, and what is it? e. Which class of car generally gets the best mileage? Explain.

Which statement about bias is true? I. Bias results from random variation and will always be present. II. Bias results from a sampling method likely to produce samples that do not represent the Population. III. Bias is usually reduced when sample size is larger.

Over the trial month the market share in the sample rose to 22% of shoppers. The company's board of directors decided this increase was significant. Now that they have concluded the new marketing campaign works, why might they still choose not to invest in the campaign?

Here is the corresponding regression table: Dependent variable is: JanTemp R squared $= 71.9 \% \quad$ R squared (adjusted) $= 71.3 \%$ $\mathrm { s } = 7.222$ with $55 - 2 = 53$ degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 7061.32 1 7061.32 135 Residual 2764.21 53 52.1549 Variable Coefficient SE(Coeff) t-ratio P-value Intercept 108.805 7.146 15.2 \leq0.0001 Lat -2.11114 0.1814 -11.6 \leq0.0001 Write a brief report based on this regression. Explain in words and numbers what this equation says about the relationship between average January low temperature and latitude. Discuss the R2 value and t-ratios.

Explain what 90% confidence means in this context.

If the diameter is increased from 4 inches to 14 inches, the predicted number of cheerios will Increase by about…

Based on the data they collected during the trial program, management found that a 95% confidence interval for the percentage of defective chips was (5.0%, 7.0%). What conclusion should management reach about the new incentive program? Explain.

Moods A headline in the New York Times announced "Research shows running can alter one's moods". The article reported that researchers gave a Personality Assessment Test to 231 males who run at least 20 miles a week, and found "statistically significant personality differences between the runners and the male population as a whole." Do you think the headline was appropriate? Explain.

Studying Assume that 75% of the Stats students studied for this test. If 40% of those who study get an A, but only 10% of those who don't study get an A, what is the probability that someone who gets an A actually studied for the test?

Based on data that she collected during the trial period the store's owner found that a 98% confidence interval for the proportion of all shoppers who might buy something was (27%, 35%). What conclusion should she reach about the mannequins? Explain.

What level of significance did management use?

What is the probability that a student from this class eats breakfast or flosses?

Design an experiment to determine if the home teams have an unfair advantage when shooting free-throws.

Find the standard deviation of the number of repairs each year.