Statistics 221 BYU-I
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx (Links to an external site.) Part 1: What is the correlation coefficient between the two variables?
-0.832
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx Part 4: In your dataset there is a vehicle that weighs 3,302 lbs. Predict the miles per gallon for that vehicle. (Remember, the regression equation is measuring weight as thousands of pounds, so 3,302 lbs. would be entered as 3.302).
-1.965
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx Part 9: What is the value of the test statistic?
-29.645
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx Part 7: What is the upper bound of your confidence interval?
-7.222
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsxA researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx (Links to an external site.) Part 3: What is the slope?
-7.647
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsxFor this and the next part construct a 90% confidence interval for the slope of the regression line. Part 6: Input the lower bound of your confidence interval.
-8.073
You would like to test if females like math more than males do. You collect a sample of 100 males and 57 females. Among the 100 males, 32 say they like math. Among the females, 21 say they like math. Use this information for all the parts. What is the p-value for your test?
.269
Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean gallons and standard deviation gallons. Part 1: What is the probability that a randomly chosen truck will have a capacity greater than 8528 gallons?
.908
Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean gallons and standard deviation gallons. Part 3: What is the probability that a sample of size 20 will have a mean between 8538 and 8550 gallons?
.975
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx Part 10: What is the P-value?
0
In the U.S., 95% of children have received their DTaP vaccine. Calculate the probability that fewer than 700 out of a sample of children received their DTaP vaccine.
0.018
An investor with a stock portfolio worth several hundred thousand dollars sued his broker and brokerage firm because he felt that lack of diversification in his portfolio led to poor performance for many years in a row. In an effort to avoid close public scrutiny, the firm agreed to settle the conflict by an arbitration panel. The arbitration panel compared a sample of 39 months of the investor's returns with the average of the Standard & Poor's stock index for the same period in order to determine whether there was a substantial decrease. The data are recorded in RatesOfReturn.xlsx (Links to an external site.). The S&P has a known population mean return of 0.95. Suppose that you are a member of this arbitration panel. Conduct a hypothesis test to determine if the investor's portfolio performed significantly worse than the performance of the S&P. Use a level of significance of . What is the P-value for this test?
0.019
Sister Smith thinks that students tend to do better in Exam 2 than in exam 1. To test her claim, you collect a random sample of 25 students and record their exam scores. The data can be found here: "Exam 1 and Exam 2 score.xlsx" (Links to an external site.). Use this data file to answer all the parts. Define the differences as Exam 1 score - Exam 2 score. Part 2: What is the p-value for your test?
0.172
Suppose you're testing against and you have calculated the test statistic to be . The area to the right of (under the standard normal density curve) is 0.091. Which one of the following is the P-value of your hypothesis test?
0.182
Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean gallons and standard deviation gallons. Part 2: Suppose that a simple random sample of tanks is selected and the sample mean capacity is found to be 8550 gallons. What is the z-score corresponding to this sample mean?
2.336
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx Part 4: In your dataset there is a vehicle that weighs 3,302 lbs. Predict the miles per gallon for that vehicle. (Remember, the regression equation is measuring weight as thousands of pounds, so 3,302 lbs. would be entered as 3.302).
20.965
You want to construct a 90% confidence interval for the population mean height of all adults in Rexburg. Assume the population is normally distributed with a population standard deviation of 20 inches. If you want a margin of error of 2 inches, how many people should you include in your study?
271
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx (Links to an external site.) Part 2: For this and the next part, compute the y-intercept and the slope of the linear regression line used to predict the miles per gallons from the weight of the vehicle (in thousands of pound). What is the y-intercept?
46.217
An entrepreneur who sells things online takes a simple random sample of internet sales transactions. Assume the (unknown) true proportion of customers who used a promo code for their purchase is 46%. The entrepreneur conducts her survey and calculates . Which of the following is the most correct interpretation of this statistic?
51.2% of the sales transactions in the sample used a promo code.
Data was obtained from a chemical process where the percent yield of the process is thought to be related to the reaction temperature (in degrees F). We would like to see if the temperature can predict the yield. The regression equation we obtained was Y = 17+ 2X. Use this information for all the parts. Part 5: Use the regression line to predict the yield of the reaction when the temperature is 32 degrees.
81
Students in an Introductory Statistics class at BYU-Idaho were studying prices of cold cereal at grocery stores in Rexburg. To get a sample of cold cereal prices, they went to Albertson's and rolled a die to decide which box from the left of the top shelf they would start on. They then recorded every 6th cereal after the first, moving from left to right down the shelves, recording the name, size, and price of each cereal in their sample. Is this study an experiment or an observational study, and why?
An observational study, because the students did not impose any treatment on the cereals.
Suppose you want to use a confidence interval to estimate the true mean number of calories found in candy bars. It is known that the distribution of the calories is normal. How many candy bars must you have in order to be sure the sampling distribution of is normal?
Any n will do
The heights of young adult females in the United States are said to have a population standard deviation of inches. A sample was taken of young adult females at BYU-Idaho and the mean was computed to be inches. A 95% confidence interval for the true mean height of females in the United States was calculated from the BYU-Idaho sample data. Which of the following explanations describes the correct way to interpret the 95% confidence interval for this problem?
Approximately 95% of all 95% confidence intervals that could be computed from the population of all adult females in the United States will contain the true mean height. We are 95% confident that the true mean height of adult females in the United States is somewhere in our confidence interval.
For the study in the previous question, the value of for the regression line was 0.05 pounds. Interpret this statistic.
As percent compliance goes up by 1 percent, the average weight lost in three months increases by 0.05 pounds.
A researcher wants to study whether or not social status of single people in the USA depends on their gender. He randomly selects 800 people and records their gender and their social status (Upper Class, Upper Middle Class, Lower Middle Class, Working Class, Poor). What type of hypothesis test would be used here?
Chi-Square test for independence
Daniel was doing a statistical study. In which step of the statistical process is he engaged when he creates a histogram of his data and calculates a sample mean?
Describe the Data
A marriage counselor conducted a study of couples, categorizing each of the couples as "communicative" or "non-communicative". Among other things, the counselor wanted to see whether the percentage of communicative couples whose marriage ended in separation or divorce was greater than the percentage of non-communicative couples whose marriage ended in separation or divorce. Which hypothesis test would be most appropriate for this study?
Difference of two proportions
Data was obtained from a chemical process where the percent yield of the process is thought to be related to the reaction temperature (in degrees F). We would like to see if the temperature can predict the yield. The regression equation we obtained was Y = 17+ 2X. Use this information for all the parts. Part 3: Interpret the slope of the regression line above.
For each degree increase in temperature, the mean yield increases by 2%.
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx Part 8: Conduct a hypothesis test to test if there is a linear relationship between the weight of the vehicles and how many miles per gallon it drives. Choose the correct null and alternative hypotheses for this analysis.
H0: B1=0 HA: B1#0
You would like to test if females like math more than males do. You collect a sample of 100 males and 57 females. Among the 100 males, 32 say they like math. Among the females, 21 say they like math. Use this information for all the parts. Part 1: What is the null and alternative hypothesis?
H0: P male=P female HA: P male<P female
Sister Smith thinks that students tend to do better in Exam 2 than in exam 1. To test her claim, you collect a random sample of 25 students and record their exam scores. The data can be found here: "Exam 1 and Exam 2 score.xlsx" (Links to an external site.). Use this data file to answer all the parts. Define the differences as Exam 1 score - Exam 2 score. Part 1: What is your null and alternative hypothesis?
H0: Ud=0 HA: Ud<0
A weight loss company wanted to predict how much weight a client would lose if they followed a prescribed exercise program in addition to the company's diet program. Volunteers were randomly divided into two groups, one group dieted but didn't exercise, and the other group dieted and followed the exercise program. For the exercise group, they used linear regression with percent compliance with the exercise program as the explanatory variable and pounds lost in three months as the response variable. One of the clients was told that his residual was 5.5 pounds. What does this mean?
His actual weight loss was 5.5 pounds higher than his predicted weight loss.
A study was conducted to measure the effectiveness of a diet program that claims to help manage weight. Subjects were randomly selected to participate. Before beginning the program, each participant was given a score based on his or her fitness level. After six months of following the diet, each participant received another score. The study wanted to test whether there was a difference between before and after scores. What confidence interval would be best in this situation?
Mean of the differences (paired samples)
A study is planned to compare the proportion of men who dislike anchovies with the proportion of women who dislike anchovies. The study seeks to determine if the proportions of men and women who dislike anchovies are different. A sample of 41 men was taken and the estimate for the true proportion of men who dislike anchovies was determined to be 0.67. A sample of 56 women was also taken and the estimate for the true proportion of women who dislike anchovies was determined to be 0.84. Are the requirements satisfied to perform this hypothesis test? Why?
No, because in at least one case .
A manufacturer claims that the thickness of the spearmint gum it produces is 7.5 one-hundredths of an inch. A quality control specialist regularly checks this claim. From his experience, the specialist knows the distribution is right skewed and that the standard deviation is 0.4 one-hundredths of an inch. On one production run, he took a random sample of n = 100 pieces of gum and measured their thickness. Which hypothesis test would be most appropriate for this task?
One mean (sigma known)
A research firm has been hired to determine the validity of claims of age discrimination made against a large multi-national corporation. They decide that the best way to do this is to randomly select employees and find their age. They randomly sample 170 employees and calculate a sample mean age of 39.9 years and a sample standard deviation 6.9 years. Which confidence interval would they use?
One mean (sigma unknown)
In the United States, mothers who live in poverty generally have babies with lower birthweight than those who do not live in poverty. The mean birthweight for babies born in the U.S. to mothers living in poverty is approximately 2800 grams. The CDC carries out a study to test the effectiveness of a new prenatal care program increasing the weight of babies born into poverty. For the study, 30 mothers, all of whom live in poverty, participate in the program and birthweight data is recorded. Which hypothesis test would be most appropriate for this study?
One mean (sigma unknown)
An attorney is investigating whether it is plausible that the percentage of Wal-Mart employees in Nevada who are over 45 years old is 30%. Which confidence interval would be most appropriate in this situation?
One proportion
The CEO of a large electric utility claims that 80 percent of his 1,000,000 customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. Among the sampled customers, 73 percent say they are very satisfied. What type of hypothesis test do we use?
One proportion
BYU-I would like to find out if the mean GPA is the same across the 6 different colleges by selecting a random sample of students from each college. What Hypothesis test would be most appropriate for them to use here?
Several means (ANOVA)
A business marketing firm specializes in radio advertising. They hope to show there is a linear relationship between sales and the amount of money a client invests in radio advertising. Which hypothesis test would be most appropriate for addressing this question?
Slope of the regression line
In order to estimate the average weight of all adults in the state of Idaho, you randomly select 50 adults from each county in Idaho. Use this information for all the parts. Part 1: What type of sampling method was done here?
Stratified Sample
Data was obtained from a chemical process where the percent yield of the process is thought to be related to the reaction temperature (in degrees F). We would like to see if the temperature can predict the yield. The regression equation we obtained was Y = 17+ 2X. Use this information for all the parts. Part 1: What would X be here?
Temperature, since it is being used to predict the yield.
You would like to compare the mean GPA between sociology majors and math majors at BYU-I. In order to do that, you select a random sample of 40 students who are Math majors and 40 who are sociology majors. Which confidence interval would be appropriate here?
The difference between two means, using independent samples.
In order to decide if a certain candidate was going to win the upcoming election, a random sample of 900 Americans were asked if they would vote for that candidate. The study showed that 46% were going to vote for him. After the election was done we found out that 51% of the votes went to that candidate. Which of the following statements is true?
The number 46% is a sample statistic. The number 51% is a population parameter.
Which of the following variables is/are quantitative?
The number of people in a randomly selected classroom on campus. The weight of a BYU-I student.
Which one of the following best describes the notion of "the significance level of a hypothesis test?"
The probability of a type I error.
Which one of the following best defines the notion of the P-value of a hypothesis test?
The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.
In order to estimate the average weight of all adults in the state of Idaho, you randomly select 50 adults from each county in Idaho. Use this information for all the parts. Part 2: What is the population in your study above?
The weights of all adults in the state of Idaho.
In the above question suppose your confidence interval was [0.32, 0.74], what does that tell you about the mean GPA of sociology majors as compared to math majors?
There is a significant difference between them.
Sister Smith thinks that students tend to do better in Exam 2 than in exam 1. To test her claim, you collect a random sample of 25 students and record their exam scores. The data can be found here: "Exam 1 and Exam 2 score.xlsx" (Links to an external site.). Use this data file to answer all the parts. Define the differences as Exam 1 score - Exam 2 score. Part 3: What is your conclusion based on the p-value you found above?
There is insufficient evidence to conclude that students tend to do better in exam 2 than they do in exam 1.
A researcher wants to see if they can predict the miles per gallons from the weight of the vehicle (in thousands of pound). The data is found in the file Vehicles.xlsx Part 11: What decision do you make based on the P-value and the level of significance (), and, thus, what do you conclude?
There is sufficient evidence to suggest that there is a linear relationship between the weight of the vehicle and the number of miles per gallon it drives.
Students were given a pre-test. Then after they listened to a certain type of music they were given a similar post test. If we define the difference as the post test score minus the pre test score and we find a 95% confidence interval for the mean of the differences to be [-1.34, 4.56]. Which of the following is true?
There seems to be insufficient evidence to show that music affected the scores since zero is in the confidence interval.
Data was obtained from a chemical process where the percent yield of the process is thought to be related to the reaction temperature (in degrees F). We would like to see if the temperature can predict the yield. The regression equation we obtained was Y = 17+ 2X. Use this information for all the parts. Part 4: Interpret the intercept of the regression line above.
When the temperature is zero degrees, the average yield is 17%.
You would like to test if females like math more than males do. You collect a sample of 100 males and 57 females. Among the 100 males, 32 say they like math. Among the females, 21 say they like math. Use this information for all the parts. Part 3: Are the requirements for the above test satisfied?
Yes, both and are larger than 10 for both groups.
A real estate company wants to evaluate two of their home appraisers for consistency in preparation for their annual state certification. It is important that different appraisers be able to give similar estimates for homes and other properties. The company selects a random sample of 10 homes in different neighborhoods around the city and independently asks each appraiser for an estimate of the home value. After they receive the estimates for each home, the company subtracts the value given by the first appraiser from the value given by the second appraiser. They create a histogram of the differences and see that it is approximately normal. Are the requirements for using the desired confidence interval satisfied? Explain.
Yes. The distribution of mean differences is normal because the sample differences have been determined to be normal.
Data was obtained from a chemical process where the percent yield of the process is thought to be related to the reaction temperature (in degrees F). We would like to see if the temperature can predict the yield. The regression equation we obtained was Y = 17+ 2X. Use this information for all the parts. Part 2: What would the response variable be here?
Yield, since it is the one being predicted.
