I am struggling with this topic. I need to know the formulas to the following questions. Any advice will be greatly appreciated!!!
1. A hospital study – which of the following statements are necessarily true?
a. The sample was stratified.
b. The treatments were applied to the groups randomly.
c. The experimenter manipulated one of the variables and observed the effects on the other variables.
d. The subjects were assigned to groups randomly.
e. The experimenter observed actions as they happened and drew conclusions from the results.
2. Match the data with name of the graph (stem & leaf, pareto, time series graph, percentiles, median, line chart histogram)
a. Display the midpoint of a data set.
b. Display the frequency distribution for categorical variables in descending order.
c. Display the distribution divided into 100 groups.
d. Display the frequency of various groups of the data while maintaining the actual data values.
3. Fifty dogs are selected at random, and their heights and weights are recorded. x =height and y = weight. Match the relationships with the appropriate description.
Strong negative relationship, strong positive relationship, weak negative relationship, weak positive relationship
a. Taller dogs are very likely to weight less than shorter dogs
b. Taller dogs are very likely to weight more the shorter dogs
c. Taller dogs weigh much less the shorter dogs sometimes.
d. Taller dogs weigh much more than shorter dogs sometimes.
e. Taller dogs are somewhat likely to weigh more the shorter dogs.
f. Taller dogs are somewhat likely to weigh less than shorter dogs.
4. One candidate for the school board has 51% of the vote, and the other has 47% of the vote. This was a telephone poll of 1,157. The margin of error is 3% at the 95% confidence level. Which statement describes the meaning of the margin of error?
a. The second candidate has between a 44% and 50% chance of winning.
b. The first candidate has a 95% change of winning.
c. There is a 95% chance that the 2nd candidate will receive between 44% and 50% of the vote.
d. The 1st candidate will win the election because they are ahead by 3% points.
5. A coin is tossed 5 times – what is the probability of obtaining exactly 3 heads?
a. 5/96
b. 1/32
c. 3/32
d. 1/16
e. 5/16
6. 100 students – 30 are taking history, 20 are taking geometry, and 10 are taking both history and geometry. What is the probability that a randomly selected student is taking history or geometry?
a. 1/5
b. 2/5
c. 3/5
d. 4/5
e. 1/2
7. What type of sampling method was used – random or non-random.
a. Employees are selected from randomly generated ID’s
b. Fifty male employees are randomly selected.
c. Clerical employees are randomly selected.
d. All Engineers are surveyed.
8. Which of the following describes an unbiased estimator?
a. An estimator that has a value that approaches the value of the parameter as the sample size increases.
b. An estimator that is equal to the value of the parameter.
c. An estimator that is not influenced by other estimators.
d. An estimator that has an expected value that is equal to the value of the parameter.
9. A plumber wishes to estimate the mean number of customers that requested emergency plumbing repairs during a 24 hour period. He selects 64 distinct 24-hour periods and determines the average number of requests. Which of the following assumptions is necessary in order for a confidence interval for the sample to be valid?
a. The sampled population has an approximate normal distribution.
b. No assumptions are necessary.
c. The sampled population has an approximate t-distribution.
d. The mean of the sample equals the mean of the population.
10. The confidence level is the mean score of students on a survey. A questionnaire has scores ranging from 0 to 200. Using a simple random sample of the students the following 95% confidence interval for the mean is computed as [887, 106]. Which of the following is safe to conclude?
a. Nothing is safe to conclude because of poor choice of sampling method.
b. If the procedure were repeated many times, approximately 95% of the resulting confidence intervals would contain the mean score of all the students.
c. The mean score of all of the students is 95.
d. 95% of the sample of students would score between 87 and 106.
e. If the procedure were repeated many times, approximately 95% of the resulting confidence intervals would contain the mean score of the sample of students.
11. To determine ice cream consumption in a town a random sample of 100 licensed drivers living in the town was conducted. 67 said they ate ice cream at least twice a month. A confidence interval for the proportion of ice cream eaters in the town is computed. Which of the following statements describes why the confidence interval might not be reliable?
a. The sample is biased by only selecting licensed drivers.
b. The sample is not large enough.
c. The population is not at least 10 times the size of the sample.
d. A confidence interval can’t be constructed unless the entire population is surveyed.
WORD PROBLEMS
1. The area of a triangle must be at least 42. The base is twice the height. Which of the following is an inequality that can be used to solve for the shortest possible base?
a. 1/2b 2h ? 42
b. 1/4b2 ? 42
c. 1/4b2 ? 42
d. 1/2bh ? 42
2. A profit of 9% was made selling books for $2,500. What was the original purchase price of the books? Which of the following will accurately solve the problem?
a. 2500 – x = 9%
b. 0.09x + x = 2500
c. 9% x x = 2500
d. x = 0.9x x 2500
e. 2500 ÷0.09 = x
3. Select the appropriate problem solving strategy: diagram, proportion or work backwards.
a. A golf course is an oval with a semicircle at each end. Find the radius of the semicircles if the total distance around the course is 500 meters.
b. A woman requires an insulin to carbohydrate ration of 1 to 15. Find the amount of insulin required for a meal of 55 carbohydrates.
c. Find the unknown number if twice the difference of three times the number and five equals 32.
d. One side of a rectangle-shaped yard is positioned along a forest. The yard requires fencing for the other three sides. The length must be three times longer than the width. Find the required perimeter of the yard to enclose an area of 500 squar
1. A hospital study – which of the following statements are necessarily true?
a. The sample was stratified.
b. The treatments were applied to the groups randomly.
c. The experimenter manipulated one of the variables and observed the effects on the other variables.
d. The subjects were assigned to groups randomly.
e. The experimenter observed actions as they happened and drew conclusions from the results.
2. Match the data with name of the graph (stem & leaf, pareto, time series graph, percentiles, median, line chart histogram)
a. Display the midpoint of a data set.
b. Display the frequency distribution for categorical variables in descending order.
c. Display the distribution divided into 100 groups.
d. Display the frequency of various groups of the data while maintaining the actual data values.
3. Fifty dogs are selected at random, and their heights and weights are recorded. x =height and y = weight. Match the relationships with the appropriate description.
Strong negative relationship, strong positive relationship, weak negative relationship, weak positive relationship
a. Taller dogs are very likely to weight less than shorter dogs
b. Taller dogs are very likely to weight more the shorter dogs
c. Taller dogs weigh much less the shorter dogs sometimes.
d. Taller dogs weigh much more than shorter dogs sometimes.
e. Taller dogs are somewhat likely to weigh more the shorter dogs.
f. Taller dogs are somewhat likely to weigh less than shorter dogs.
4. One candidate for the school board has 51% of the vote, and the other has 47% of the vote. This was a telephone poll of 1,157. The margin of error is 3% at the 95% confidence level. Which statement describes the meaning of the margin of error?
a. The second candidate has between a 44% and 50% chance of winning.
b. The first candidate has a 95% change of winning.
c. There is a 95% chance that the 2nd candidate will receive between 44% and 50% of the vote.
d. The 1st candidate will win the election because they are ahead by 3% points.
5. A coin is tossed 5 times – what is the probability of obtaining exactly 3 heads?
a. 5/96
b. 1/32
c. 3/32
d. 1/16
e. 5/16
6. 100 students – 30 are taking history, 20 are taking geometry, and 10 are taking both history and geometry. What is the probability that a randomly selected student is taking history or geometry?
a. 1/5
b. 2/5
c. 3/5
d. 4/5
e. 1/2
7. What type of sampling method was used – random or non-random.
a. Employees are selected from randomly generated ID’s
b. Fifty male employees are randomly selected.
c. Clerical employees are randomly selected.
d. All Engineers are surveyed.
8. Which of the following describes an unbiased estimator?
a. An estimator that has a value that approaches the value of the parameter as the sample size increases.
b. An estimator that is equal to the value of the parameter.
c. An estimator that is not influenced by other estimators.
d. An estimator that has an expected value that is equal to the value of the parameter.
9. A plumber wishes to estimate the mean number of customers that requested emergency plumbing repairs during a 24 hour period. He selects 64 distinct 24-hour periods and determines the average number of requests. Which of the following assumptions is necessary in order for a confidence interval for the sample to be valid?
a. The sampled population has an approximate normal distribution.
b. No assumptions are necessary.
c. The sampled population has an approximate t-distribution.
d. The mean of the sample equals the mean of the population.
10. The confidence level is the mean score of students on a survey. A questionnaire has scores ranging from 0 to 200. Using a simple random sample of the students the following 95% confidence interval for the mean is computed as [887, 106]. Which of the following is safe to conclude?
a. Nothing is safe to conclude because of poor choice of sampling method.
b. If the procedure were repeated many times, approximately 95% of the resulting confidence intervals would contain the mean score of all the students.
c. The mean score of all of the students is 95.
d. 95% of the sample of students would score between 87 and 106.
e. If the procedure were repeated many times, approximately 95% of the resulting confidence intervals would contain the mean score of the sample of students.
11. To determine ice cream consumption in a town a random sample of 100 licensed drivers living in the town was conducted. 67 said they ate ice cream at least twice a month. A confidence interval for the proportion of ice cream eaters in the town is computed. Which of the following statements describes why the confidence interval might not be reliable?
a. The sample is biased by only selecting licensed drivers.
b. The sample is not large enough.
c. The population is not at least 10 times the size of the sample.
d. A confidence interval can’t be constructed unless the entire population is surveyed.
WORD PROBLEMS
1. The area of a triangle must be at least 42. The base is twice the height. Which of the following is an inequality that can be used to solve for the shortest possible base?
a. 1/2b 2h ? 42
b. 1/4b2 ? 42
c. 1/4b2 ? 42
d. 1/2bh ? 42
2. A profit of 9% was made selling books for $2,500. What was the original purchase price of the books? Which of the following will accurately solve the problem?
a. 2500 – x = 9%
b. 0.09x + x = 2500
c. 9% x x = 2500
d. x = 0.9x x 2500
e. 2500 ÷0.09 = x
3. Select the appropriate problem solving strategy: diagram, proportion or work backwards.
a. A golf course is an oval with a semicircle at each end. Find the radius of the semicircles if the total distance around the course is 500 meters.
b. A woman requires an insulin to carbohydrate ration of 1 to 15. Find the amount of insulin required for a meal of 55 carbohydrates.
c. Find the unknown number if twice the difference of three times the number and five equals 32.
d. One side of a rectangle-shaped yard is positioned along a forest. The yard requires fencing for the other three sides. The length must be three times longer than the width. Find the required perimeter of the yard to enclose an area of 500 squar