unit test review
A farmer would like to estimate the mean amount of corn produced on the east side of his farm versus the west side of his farm where the soil is different. To do so, he selects a random sample of 20 of the 400 plots of land on the east side of the farm and randomly selects 10 plots of land from the 150 plots on the west side of his farm and measures the amount of corn produced for each plot. Are the conditions for inference met?
No, the Normal/large sample condition is not met for both samples.
The owner of an apple orchard would like to estimate the mean number of usable apples produced per tree in his large orchard. He selects a random sample of 10 trees from his large orchard. This dotplot displays the number of usable apples produced for each of these trees. Are the conditions for constructing a t confidence interval met?
No, the Normal/large sample condition is not met.
A study seeks to estimate the difference in the mean fuel economy (measured in miles per gallon) for vehicles under two treatments: driving with underinflated tires versus driving with properly inflated tires. To quantify this difference, the manufacturer randomly selects 12 cars of the same make and model from the assembly line and then randomly assigns six of the cars to be driven 500 miles with underinflated tires and the other six cars to be driven 500 miles with properly inflated tires. The dotplots show the data.
Yes, all three conditions for inference are met.
A random sample of 30 students is selected. Each student is asked to report how much time they spent the previous night on math homework and how much time they spent on science homework. A 95% confidence interval for the true mean difference (math - science) in the amount of time spent on homework is 30 minutes to 75 minutes. A science teacher claims that students tend to spend more time working on math homework than on science homework. Is this claim supported by the 95% confidence interval?
Yes, the confidence interval consists entirely of positive numbers.
A researcher is 95% confident that the interval from 5.8 minutes to 9.3 minutes captures the true mean amount of time it takes to pump a full tank of gas in a certain type of SUV.
Yes, this is a plausible value for the population mean, because 9 is within the 95% confidence interval.
A junior at a large high school wants to estimate the amount of time it takes to log in to a school computer. He randomly selects 35 students and records the amount of time it takes to log in. The junior constructs a 95% confidence interval for the true mean amount of time it takes to log in to a school computer. Which of the following would decrease the margin of error?
constructing a 90% confidence interval
A social worker at a large high school wants to estimate the number of days students are absent. He randomly selects 45 students and records the number of days each one is absent. The social worker constructs a 95% confidence interval for the true mean number of days students at this school are absent. Which of the following would decrease the margin of error?
constructing a 90% confidence interval
An athletic trainer would like to estimate how many additional calories are burned when completing a high intensity interval training (HIIT) workout for 30 minutes rather than doing yoga for 30 minutes. A group of 30 volunteers are randomly assigned to take a 30-minute HIIT class or a 30-minute yoga class wearing a calorie-counting armband. A 90% confidence interval for the true difference in the population means is 157.23 calories to 210.91 calories. Based upon the confidence interval, is it reasonable to claim that doing 30 minutes of a HIIT workout burns 250 more calories than doing a 30-minute yoga workout?
no because 250 is not in the confidence interval
A study seeks to estimate the difference in the mean fuel economy (measured in miles per gallon) for vehicles under two treatments: driving with underinflated tires versus driving with properly inflated tires. To quantify this difference, the manufacturer randomly selects 12 cars of the same make and model from the assembly line and then randomly assigns six of the cars to be driven 500 miles with underinflated tires and the other six cars to be driven 500 miles with properly inflated tires. What is the appropriate inference procedure?
t confidence interval for a difference in means
A farmer would like to estimate the mean amount of milk produced per day by his 300 cows. He selects a random sample of 15 cows and records the amount of milk produced (in gallons) by those cows. The dotplot shows the data. Given that all of the recorded values are integers, what is the value of the standard error of the mean?
0.765
A group of six students decides to conduct an experiment about "brain freeze," a phenomenon that often occurs when eating something cold. The students each flip a coin. If they flip heads, they eat a cup of Italian ice as fast as they can while sitting in an air-conditioned car. If they flip tails, they eat a cup of Italian ice as fast as they can while sitting outside in the sunshine. After a recovery period, they each complete the opposite treatment. The students record the amount of time it takes, in seconds, for them to experience brain freeze under each condition. The data are displayed in the table. What is the mean difference (sun - car) and the standard deviation of the differences?
B
A teacher would like to estimate the mean amount of time it takes for students taking this statistics class to complete this multiple-choice assessment item. To do so, she selects a random sample of 50 students enrolled in this statistics class and records the amount of time (in minutes) it takes them to complete this question. The standard error of the mean is 0.27 minutes. What is the interpretation of the standard error of the mean?
If we select many random samples of students enrolled in this statistics class, the sample mean amount of time needed to complete this question would typically vary by about 0.27 minutes from the population mean.
A random sample of 100 customers is selected, and the mean difference in their satisfaction rating for company A and company B is calculated. A rating of 1 indicates that a customer is highly dissatisfied, and a rating of 5 indicates that a customer is highly satisfied. A 90% confidence interval for the true mean difference (company A - company B) in satisfaction ratings is -2.5 to 1.5. Based on the confidence interval, the owner of company B claims that customers are more satisfied with his company than with company A. Is this claim supported by the 90% confidence interval?
No, the confidence interval does not consist entirely of negative numbers.
A varsity swimmer at a large high school wants to estimate the amount of time (in hours), on average, athletes at this school train or practice each day. This swimmer selects 10 members of her swim team and asks them how many hours they typically train or practice. Use the data to construct a 90% confidence interval to estimate the true mean number of hours athletes at this school train or practice each day. Have the conditions for inference been met?
No, the sample is not random.
A doctor would like to estimate the mean difference in height of pairs of identical twins. The doctor randomly selects 8 pairs of identical twins and determines the current height, in inches, of each twin. The data are displayed in the table. The conditions for inference are met. The 95% confidence interval for the mean difference (twin 1 - twin 2) in height is (-0.823, 0.573). What is the correct interpretation of this interval?
The doctor can be 95% confident that the interval from -0.823 inches to 0.573 inches captures the true mean difference in the height of twins.
