Unit Test — Unit test Answers

A real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged,” meaning filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the five staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers.

A local athletic facility offers a four-week training course, hoping to increase athletes’ running speeds. Thirty-five volunteer athletes are timed, in seconds, running a 50-yard dash before the training program begins and then again after the program is complete. The difference in running times (before training – after training) is calculated for each athlete. What are the hypotheses the facility should use?

The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 50 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. A significance test at an alpha level of produces a P-value of 0.02. What is the correct interpretation of the P-value?

In an effort to improve scores on college-entrance exams, the principal at a large high school chooses 35 students at random who have already taken the exam. The students are enrolled in a six-week prep course to improve their scores. After the prep course, the students take the college-entrance exam again. The mean difference (first – second) in exam scores is –1.75 points with a standard deviation of 7.12 points. Assuming the conditions for inference are met, what is the test statistic for testing the hypotheses ?

A personal trainer determines that an individual will get the most benefit from a workout if they keep their heart rate at an average of 150 beats per minute during workouts. To determine if the individual is doing so successfully, a random sample of 30 workouts is selected from their fitness watch. A 95% confidence interval for these workouts reveals that the true mean heart rate while working out is between 158 and 167 beats per minute. Based upon this interval, what conclusion should be made about the hypotheses: = 150 versus 150 where μ = this individual’s true mean heart rate during working out at α = 0.05?

The daily temperatures in fall and winter months in Virginia have a mean of 62o F. A meteorologist in southwest Virginia believes the mean temperature is colder in this area. The meteorologist takes a random sample of 30 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 59oF with a standard deviation of 6.21oF. Do the data provide convincing evidence at the level that the mean temperature in fall and winter months in southwest Virginia is less than 62o F?

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value?Find the t-table here.

A company that makes robotic vacuums claims that their newest model of vacuum lasts, on average, two hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of five vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. Here are the data (in hours): 2.2, 1.85, 2.15, 1.95, and 1.90. They would like to know if the data provide convincing evidence that the true mean run time differs from two hours. The consumer group plans to test the hypotheses H0: μ = 2 versus Ha: μ ≠ 2, where μ = the true mean run time for all vacuums of this model. Are the conditions for inference met?

A real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged,” meaning they were filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers.

On average, a person’s body temperature should be approximately 98.6°F. A doctor would like to test the hypotheses = 98.6 versus 98.6 where μ = the true mean body temperature of all adults. Before conducting the test, the doctor determines that the power of the test to reject the null hypothesis when μ = 98 using α = 0.01 and n = 10 is 0.2474. What combination of sample size and significance level would increase the power of this test the most?

A company that sells hair-care products wants to determine if a product that combines shampoo and conditioner works better than a shampoo and conditioner used separately. A researcher recruits 60 volunteers and pairs them according to age, hair color, and hair type. For each pair, the researcher flips a coin to determine which volunteers will use the shampoo/conditioner combination and which ones will use the separate shampoo and conditioner. After using the products for one month, the subjects are asked to rate their satisfaction with the hair products on a scale of 1–10 (1 = highly dissatisfied and 10 = highly satisfied).

From previous experience, the owner of an apple orchard knows that the mean weight of gala apples is 140 grams. This year there has been more precipitation than usual and the owner believes the weights of the apples will be heavier than usual. The owner takes a random sample of 30 apples and records their weights.What is the appropriate inference procedure?

On the SAT exam, a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes. What are the appropriate hypotheses?

A teacher has two large containers, A and B, filled with blue, red, and green beads. She wants her students to estimate the difference (A – B) in the proportion of red beads in each container.What is the appropriate inference procedure?

A local athletic facility offers a four-week training course, hoping to increase athletes’ running speeds. Thirty-five volunteer athletes are timed, in seconds, running a 50-yard dash before the training program begins and then again after the program is complete. The difference in running times (before training – after training) is calculated for each athlete. Are the conditions for inference met?

On the SAT exam, a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam. The conditions for inference are met. The test statistic is t = –1.85 and the P-value is between 0.025 and 0.05. What conclusion should be made at the significance level, ?

On a college entrance exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The counselor would like to know if there is convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses = 25 versus < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

A high school senior wonders if being blindfolded affects a person’s typing accuracy. He randomly selects 17 students from his large school. For one of the treatments, the senior reads a statement to each student and asks them to type it while wearing a blindfold. For the other treatment, the student is asked to type a similar statement without wearing a blindfold. The order of treatments is determined with the flip of a coin. The mean difference (blindfolded – not blindfolded) in the number of correct words is 6.12 words with a standard deviation of 5.98 words.

A refrigeration unit at a restaurant is supposed to be kept at 40°F. An inspector would like to test the hypotheses = 40 versus 40 where μ = the true mean temperature for all times of the day. A 98% confidence interval based upon a random sample of 40 temperatures is 40.5 degrees to 42.1 degrees. Using the interval, what decision should be made?

A shoe company wants to determine if the new tread on its top line of running shoes lasts longer than the original tread. The company recruits 50 runners for a study. Each runner will perform their typical workout wearing one shoe with the original tread on one foot and another shoe with the new tread on the other foot. The foot that wears the new type of tread will be decided by flipping a coin. After one month, the runner will wear the new type of tread on the opposite foot. At the end of the second month, the difference in tread wear (New – Original) will be calculated. The company will then estimate the mean difference in the treads.