Unit Test — Unit test Answers

A certain oat cereal manufacturer boasts that adults who eat its cereal every day have lower cholesterol levels. To test this claim, a nurse measures the cholesterol levels of 18 patients. These patients are instructed to eat the oat cereal every day for four weeks. At the end of this four-week period, the nurse measures the cholesterol levels again. The differences in cholesterol levels (before – after) are listed. A negative difference means that a patient’s cholesterol level increased over the four weeks.–18, 5, 9, –1, 0, 4, 3, –2, 0, 11, 5, 12, –5, 1, –3, 4, 8, 9

The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3.54 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of tests the hypotheses pounds; pounds. What is the consequence of a Type II error in this situation?

Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. What are the appropriate hypotheses?

A student wants to determine the proportion of times a spun penny will land on heads. She spins a penny 50 times and records the number of times it lands on heads. What type of sampling is described in this study?

The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3.54 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of tests the hypotheses pounds; pounds. What is a Type II error in this situation?

A certain oat cereal manufacturer boasts that adults who eat its cereal every day have lower cholesterol levels. To test this claim, a nurse measures the cholesterol levels of 18 patients. These patients are instructed to eat the oat cereal every day for four weeks. At the end of this four-week period, the nurse measures the cholesterol levels again. The differences in cholesterol levels (before – after) are listed. A negative difference means that a patient’s cholesterol level increased over the four weeks.–18, 5, 9, –1, 0, 4, 3, –2, 0, 11, 5, 12, –5, 1, –3, 4, 8, 9

A drug manufacturing company believes it has found a new medication to alleviate pain for headache sufferers. Twenty people with chronic headaches are asked to take a placebo pill or a pill containing the new medication during their next headache episode. The pill they take is determined by a coin flip. An hour later, the participants are asked to rate their headache pain level on a scale from 1 (no pain) to 5 (severe pain). During their next headache episode, the subjects are asked to take the other pill. The difference in pain ratings (new pill – placebo) is calculated for each subject. Are the conditions for inference met?

The daily temperatures in fall and winter months in Virginia have a mean of 62oF. 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?

The amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. A student claims that the average travel time to school for his large district is 20 minutes. To further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22.4 minutes with a standard deviation of 5.9 minutes. He would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. The student would like to test H0: μ = 20 versus Ha: μ > 20, where μ = the true mean travel time for all students who attend this school. The conditions for inference are met. The test statistic is t = 2.88 and the P-value is between 0.0025 and 0.005. What conclusion should be made at the significance level, ?

Can a person train to become better at holding their breath? An experiment was designed to find out. Twelve volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds)Group 1: 90, 88, 70, 110, 75, 105Group 2: 40, 48, 35, 50, 55, 62

Can a person train to become better at holding their breath? An experiment was designed to find out. A group of 12 volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds):Group 1: 90, 88, 70, 110, 75, 105Group 2: 40, 48, 35, 50, 55, 62

An economics major believes that in married couples, the taller spouse has the higher income. To test this theory, she randomly selects 26 married couples and records their yearly incomes. The mean difference (taller – shorter) in incomes is $1,668 with a standard deviation of $1,290.

Can you train yourself to become better at holding your breath? An experiment was designed to find out. A group of 12 volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds):Group 1: 90, 88, 70, 110, 75, 105Group 2: 40, 48, 35, 50, 55, 62

The mayor of a large town wants to estimate the proportion of households in the town that would support a proposal. The mayor’s assistant randomly selects 100 households and asks whether they would support the mayor’s proposal. Sixty households responded that they would.What is the appropriate inference procedure?

The amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. A student claims that the average travel time to school for his large district is 20 minutes. To further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22.4 minutes with a standard deviation of 5.9 minutes. He would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. The student would like to test H0: μ = 20 versus Ha: μ > 20, where μ = the true mean travel time for all students who attend this school. The conditions for inference are met. What are the appropriate test statistic and P-value?Find the t-table here.