Test 6 Review
In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Calculate the linear correlation coefficient.
.981
Given the length of a human's femur, x, and the length of a human's humerus, y, would you expect a positive correlation, a negative correlation, or no correlation?
positive correlation
Which of the following provides the most reasonable approximation to the least squares regression line?
y ˆ = 50 + 10x
Which correlation coefficient best describes the relation depicted in the scatter-plot?
-0.7
A sociologist was interested in determining if there was a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the 5% level of significance. Provided the assumptions of the test are satisfied, find the expected number of 24-29 year-olds who prefer comedies under the null hypothesis.
10.29
A sociologist was interested in determining if there was a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the 5% level of significance. Provided the assumptions of the test are satisfied, find the test statistic χ2.
3.623
A sociologist was interested in determining if there was a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the 5% level of significance. Provided the assumptions of the test are satisfied, determine the critical value for the test.
9.488
A university statistician found that the correlation between college GPA and starting salary was 0.12. Based on this you would tell the university that:
GPA is a poor predictor of starting salary
A study was conducted to determine if there is a relationship between fan preference of instant replay use and the sport in which it is applied. The category counts of 102 fans are provided in the two-way table below. Use a Chi-Square independence test to determine if fan preference of instant replay use and the sport in which it is applied are independent at the 5% level of significance. State the null and alternative hypotheses. Provided the assumptions of the test are satisfied, state your conclusion to the test. Note: the test statistic is 16.629
H0: Instant replay preference is independent of sport.HA: Instant replay preference is dependent of sport.
It has been rumored that the color distribution of M&M's is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green. You suspect this rumor is incorrect and decide to count how many of each color are contained in a randomly chosen bag in order to perform a Chi-Square goodness-of-fit test at a 5% significance level. State the null and alternative hypotheses.
H0: pbrown=0.30 , pyellow=0.20 , pred=0.20 , porange=0.10 , pblue=0.10 , pgreen=0.10HA: At least one of the stated proportions is not correct.
A sociologist was interested in determining if there was a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the 5% level of significance. State the Null Hypothesis.
Ho: Age and type of movie preferred are independent. Ha: Age and type of movie preferred are dependent.
A local retailer currently schedules employees based on the assumption that they serve customers uniformly throughout the week (the same number each day). Management is starting to question this assumption and decides to collect data on the number of customers served each day of the week to perform a Chi-Square goodness-of-fit test at a 5% significance level.
Ho: Customers are distributed evenly throughout the week. Ha: Customers are not distributed evenly throughout the week.
A sociologist was interested in determining if there was a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the 5% level of significance. Provided the assumptions of the test are satisfied, state your conclusion to the test. Note: the p-value = 0.4594
The data does not suggest that age and type of movie preferred are dependent.
In which scatter diagram is r = 0.01?
upward
Each year U.S. News and World Report conducts its "Survey of America's Best Graduate and Professional Schools." and ranks the top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. The results of a simple linear regression of SALARY versus GMAT using the 25 data points are shown below. Is there sufficient evidence to suggest there is a linear relationship between SALARY and GMAT at the 5% level of significance?
There is enough evidence (at α = .05) to suggest that there is a linear relationship between SALARY and GMAT.
In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. Find the equation of the regression line for the given data.
^ y = 6.910x + 46.261
A local retailer currently schedules employees based on the assumption that they serve customers uniformly throughout the week (the same number each day). Management is starting to question this assumption and decides to collect data on the number of customers served each day of the week to perform a Chi-Square goodness-of-fit test at a 5% significance level. Provided the assumptions of the test are satisfied, calculate the test statistic χ2.
13.45
A local retailer currently schedules employees based on the assumption that they serve customers uniformly throughout the week (the same number each day). Management is starting to question this assumption and decides to collect data on the number of customers served each day of the week to perform a Chi-Square goodness-of-fit test at a 5% significance level. Provided the assumptions of the test are satisfied, determine the expected number of customers served each day under the null hypothesis.
30 X
In an area of the Midwest, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Which is the best predicted value for y given x = 7.1? Assume that the variables x and y have a significant correlation.
35.4
If the correlation between a person's age and annual income is r=0.60, what does the coefficient of determination r 2 tell us about the explained variation?
36% of the variation in a person's annual income can be explained by the predictor variable age.
It has been rumored that the color distribution of M&M's is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green. You suspect this rumor is incorrect and decide to count how many of each color are contained in a randomly chosen bag in order to perform a Chi-Square goodness-of-fit test at a 5% significance level. Provided the assumptions of the test are satisfied, calculate the test statistic χ2.
4.15, Fail to Reject Ho
A local retailer currently schedules employees based on the assumption that they serve customers uniformly throughout the week (the same number each day). Management is starting to question this assumption and decides to collect data on the number of customers served each day of the week to perform a Chi-Square goodness-of-fit test at a 5% significance level
3.84 X
A study was conducted to determine if there is a relationship between fan preference of instant replay use and the sport in which it is applied. The category counts of 102 fans are provided in the two-way table below. Use a Chi-Square independence test to determine if fan preference of instant replay use and the sport in which it is applied are independent at the 5% level of significance. Provided the assumptions of the test are satisfied, state your conclusion to the test. Note: the test statistic is 16.629 Provided the assumptions of the test are satisfied, state your conclusion to the test. Note: the test statistic is 16.629
Instant Replay Preference is dependent on Sport.
A store manager conducted an experiment in which he systematically varied the width of a display for toothpaste from 3 ft. to 6 ft. and recorded the corresponding number of tubes of toothpaste sold per day. The data was used to build a regression line, which was: tubes sold per day = 20 + 10(display width) What is the predicted number of tubes sold per day for a display width of 12 feet?
It would be unwise to use the regression line to make a prediction for a display width of 12 ft.
A local retailer currently schedules employees based on the assumption that they serve customers uniformly throughout the week (the same number each day). Management is starting to question this assumption and decides to collect data on the number of customers served each day of the week to perform a Chi-Square goodness-of-fit test at a 5% significance level. Provided the assumptions of the test are satisfied, state your conclusion to the test.
There is sufficient evidence to conclude that customers are unevenly distributed throughout the week.
