What are the hypotheses the teacher should use?
The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than volunteers without training. Let mu sub 1 is equal to the true mean amount of time that volunteers who were given training held their breath and mu sub 2 is equal to the true mean amount of time that volunteers without training held their breath. What are the appropriate hypotheses?
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 open paren before training minus after training close paren is calculated for each athlete. What are the hypotheses the facility should use?
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 percent 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: ratio of cap h sub 0 to mu is equal to 150 versus ratio of cap h sub A to mu is not equal to 150 where μ= this individual’s true mean heart rate during working out at α=0.05 ?
From previous experience, the owner of an apple orchard knows that the mean weight of Gala apples is 140 grams. There has been more precipitation than usual this year. The owner believes the weights of the apples will be heavier than usual and therefore the crop will be more profitable. This will allow the owner to expand the orchard. The owner takes a random sample of 30 apples and records their mean weight. What is the consequence of a Type I error in this situation?
The daily temperatures in fall and winter months in Virginia have a mean of 62 times degree 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 59 times degree F with a standard deviation of 6 point 2 1 times degree F Do the data provide convincing evidence at the alpha is equal to 0 point 0 5 level that the mean temperature in fall and winter months in southwest Virginia is less than 62 times degree F ? What is the test statistic for this significance test?
On average, a person’s body temperature should be approximately 98 point 6 times degree F A doctor would like to test the hypotheses ratio of cap h sub 0 to mu is equal to 98 point 6 versus ratio of cap h sub A to mu is not equal to 98 point 6 where mu is equal to 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 mu is equal to 98 using alpha is equal to 0 point 0 1 and n is equal to 10 is 0 point 2 4 7 4 What combination of sample size and significance level would increase the power of this test the most?
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 point 2 comma 1 point 8 5 comma 2 point 1 5 comma 1 point 9 5 , and 1 point 9 0 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 ratio of cap h sub 0 to mu is equal to 2 versus ratio of cap h sub A to mu is not equal to 2 , where mu is equal to the true mean run time for all vacuums of this model. Are the conditions for inference met?
The distribution of professional baseball player salaries has a mean of 3 point 2 dollars 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 point 9 dollars million with a standard deviation of 2 point 1 dollars million. A significance test at an alpha level alpha is equal to 0 point 0 5 of produces a cap p -value of 0 point 0 2 What is the correct interpretation of the cap p -value?
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 dollars comma 000 with a standard deviation of 22 dollars comma 000 The mean selling price of the five staged homes was 175 dollars comma 000 with a standard deviation of 35 comma 000 A dotplot of each sample shows no strong skewness and no outliers. The agent tests ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is less than 0 , where mu sub 1 is equal to the true mean selling price of all comparable empty homes and mu sub 2 is equal to the true mean selling price of all comparable staged homes. Are the conditions for inference met for carrying out a t - test for a difference in means?
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 dollars comma 000 with a standard deviation of 22 dollars comma 000 The mean selling price of the 5 staged homes was 175 dollars comma 000 with a standard deviation of 35 comma 000 A dotplot of each sample shows no strong skewness and no outliers. Let mu sub 1 is equal to the true mean selling price of all empty homes and mu sub 2 is equal to the true mean selling price of all staged homes. What are the appropriate hypotheses?
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 point 5 minutes with a standard deviation of 4 point 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?
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 ratio of cap h sub 0 to mu is equal to 25 versus ratio of cap h sub A to mu is less than 25 , where mu is equal to the true mean amount of time needed by students at this school to complete this portion of the exam. The power of this test to reject the null hypothesis when mu is equal to 24 point 5 is 0 point 7 3 5 What could the counselor have done to increase the power of this test?
A teacher has two large containers, cap A and cap b , filled with blue, red, and green beads. She wants her students to estimate the difference open paren cap A minus cap b close paren in the proportion of red beads in each container. What is the appropriate inference procedure?
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 open paren New minus Original close paren will be calculated. The company will then estimate the mean difference in the treads. 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 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 point 5 minutes with a standard deviation of 4 point 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 ratio of cap h sub 0 to mu is equal to 25 versus ratio of cap h sub A to mu is less than 25 , where mu is equal to 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 cap p -value? Use the t -table.
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 open paren first minus second close paren in exam scores is negative 1 point 7 5 points with a standard deviation of 7 point 1 2 points. Assuming the conditions for inference are met, what is the test statistic for testing the hypotheses ratio of cap h sub 0 to mu sub diff is equal to 0 ; ratio of cap h sub A to mu sub diff is less than 0 ?
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