Statistics Unit 3

A small business owner has created a linear regression model to predict the number of new customers who will visit a shop based on the number of times the owner has an advertisement played on the radio. What is the explanatory variable and what is the response variable?

• Explanatory: number of new customers; response: number of times the advertisement is played

• Explanatory: number of times the advertisement is played; response: number of new customers

• Explanatory: number of times the advertisement is played; response: number of purchases made by customers

• Explanatory: number of purchases made by customers; response: number of times the advertisement is played

• Explanatory: number of previous customers; response: number of new customers

Bankers at a large financial institution created the linear regression model d=0.37−0.0004s to predict the proportion of customers who would default on their loans, d, based on the customer’s credit score, s.

For a customer with a credit score of 700, which of the following is true?

• The default proportion is predicted to be 0.09.

• The default proportion will be 0.09.

• The default proportion is predicted to be approximately 1.75 million.

• The default proportion will be approximately 1.75 million.

• The default proportion is predicted to be 0.28.

A marketing consultant, Sofia, has been studying the effect of increasing advertising spending on product sales. Sofia conducts several experiments, each time spending less than $1,000 in advertising. When she analyzed the relationship between x = advertising spending and y= product sales, the relationship was linear with r=0.90. Her boss is thrilled and asks her to estimate product sales for $100,000 in advertising spending. Is it appropriate for her to calculate a predicted amount of product sales with advertising spending of $100,000?

• Yes, because the association is linear.

• Yes, because the association is positive.

• Yes, because the association is strong.

• No, because the value of the correlation is not equal to 1.

• No, because $100,000 is much greater than the values used in the experiment.

The following is a residual plot from a regression of a variable with the independent variable x.

Based on the plot, is it reasonable to conclude that a linear model is appropriate?

• Yes, because the plot shows no apparent pattern.

• Yes, because the points in the plot display less variation as x

  increases.

• Yes, because the sum of the residuals is close to zero..

• No, because the plot shows no apparent pattern.

• No, because the points in the plot display more variation as x

  increases.

What is Ms. WuRohe's husband's name?

• Joe

• Jimmy

• Jason

• Jake

The following scatterplot shows the ages, in years, of 12 of the wealthiest people in the world along with their net worth, in billions of dollars. The data point at age 83 is labeled Q.

Suppose point Q is removed from the data set. Which of the following is likely not affected by the removal?

• The correlation coefficient

• The sign of the slope coefficient

• The value of the slope coefficient

• The sum of the squared residuals

• The net worth intercept

Kristen is investigating the opinions of students at her high school on the new school hours proposed by the school board. Which of the following is her population of interest?

• All members of the school board

• All teachers at her school

• All students at her high school

• All students in the school district

• All high school students in the state

A sample of students will be selected from all the students at a high school. Which of the following sampling methods is least likely to produce a representative sample of the students?

• From a list of all student names, randomly select 50 names from the list for the sample.

• Randomly choose five classrooms in the school and use all the students in those classrooms for the sample.

• Divide the students into the four class years (freshman, sophomore, junior, senior) and randomly select students from each year in proportion to the number of students in each year.

• From a numbered list of all student names, randomly choose a starting point and then choose every tenth student on the list.

• From a randomly chosen home basketball game, choose every tenth student who enters the gymnasium.

The manager of a shopping mall distributed a customer-satisfaction survey by handing it to people as they came through one of the doors to the mall one day. Of those handed out, 215 were completed and returned. Should the results of the survey be generalized to the population of all customers of the shopping mall?

• Yes, because the sample size is large.

• Yes, because only people entering the mall were given the survey.

• Yes, because the sample was representative.

• No, because a random sample from all customers of the shopping mall was not selected.

• No, because not all customers were selected.

Which of the following is a benefit to using a random sample for an observational study?

• The random sample allows for different treatments to be assigned.

• A causal relationship can be determined.

• The results of the observational study can be generalized to the population.

• A random sample is the easiest method of data collection.

• The distribution of the sample will match the distribution of the population.