Math 11: Statistics
Identify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 15,000 households, and the data collected over the next 7 years will be used to determine whether the proportion of households tuned to a particular news program decreases. Which type of observational study is described in the problem statement?
A prospective study
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of a gender selection method used to increase the likelihood of a baby being born a girl, 1921 users of the method gave birth to 940 boys and 981 girls. There is about an 18% chance of getting that many girls if the method had no effect.
Because there is an 18% chance of getting that many girls by chance, the method does not have statistical significance. Not many couples would likely use a procedure that raises the likelihood of a girl from the approximately 50% rate expected by chance to the 51% produced by this method. So this method does not have practical significance.
Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their pricing, Greyhound Lines randomly selects 70 busses during a certain week and surveys all passengers on the busses.
Cluster
Determine whether the description corresponds to an observational study or an experiment. Fifty patients with colon cancer are divided into two groups. One group receives an experimental drug to fight cancer, the other a placebo. After one year, the spread of the cancer is measured.
Experiment
A report about the decline of Western investment in the third world countries included: "After years of daily flights, several European airlines halted passenger service. Foreign investment fell 250 during the 1990s, What is wrong with this statement?
If foreign investment fell by 100%, it would be totally eliminated, so it not possible for it to fall by more than 100%
Explain the difference between a single-blind and a double-blind experiment
In a single-blind experiment, the subject does not know which treatment is received. In a double-blind experiment, neither the subject nor the researcher in contact with the subject knows which treatment is received.
Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 696 human resource professionals, each was asked about the importance of the age of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.
It appears to be sound because the data are not biased in any way.
A study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.) What percentage of the 5000 surveys were returned? Does that response rate appear to be low? In general, what is a problem with a very low response rate? What is a problem with a very low response rate?
Of the 5000 surveys, 14% were returned. This response rate appears to be low. It creates a serious potential for getting a biased sample that consists of those with a special interest in the topic.
Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. A large company wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 40 customers and asks them about their level of satisfaction with the company.
Random
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A woman experienced a tax audit. The tax department claimed that the woman was audited because she was randomly selected from all the taxpayers. nothing nothing nothing
Random sampling
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A woman is selected by a marketing company to participate in a paid focus group. The company says that the woman was selected because she was randomly chosen from all women in her tax bracket.
Stratified sampling
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the hair colors of respondents are identified as 1 for brown hair comma 2 for blond hair comma 3 for black hair comma and 4 for anything else. The average (mean) is calculated for 680 respondents and the result is 1.5 . What is wrong with the given calculation?
The data are at the nominal level of measurement. Such data are not counts or measures of anything, so it makes no sense to compute their average (mean).
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a set of data, alert levels are represented as 1 for low, 2 for medium, and 3 for high. The average (mean) of the 573 alert levels is 1.3 . What is wrong with the given calculation?
The data are at the ordinal level of measurement. Such data should not be used for calculations such as an average.
State whether the data described below are discrete or continuous, and explain why. The volumes (in cubic feet) of different rooms
The data are continuous because the data can any value in an interval
State whether the data described below are discrete or continuous, and explain why. The exact mass left parenthesis in grams right parenthesis of food eaten by a person each day
The data are continuous because the data can take on any value in an interval.
State whether the data described below are discrete or continuous, and explain why. The numbers of channels on different televisions
The data are discrete because the data can only take on specific values.
Determine whether the data described below are qualitative or quantitative and explain why. The weights of subjects in a clinical trial of a new drug
The data are quantitative because they consists of counts or measurements
Determine whether the given description corresponds to an observational study or an experiment. In a study of 353 women with a particular disease, the subjects were asked to complete a survey about their diet upon arrival to a hospital.
The given description corresponds to an observational study.
Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on 50 different days, and the average (mean) value is 132.5 volts.
The given value is a statistic for the year because the data collected represent a sample.
Identify which of these designs is most appropriate for the given experiment: completely randomized design, randomized block design, or matched pairs design. A drug is designed to treat insomnia. In a clinical trial of the drug, amounts of sleep each night are measured before and after subjects have been treated with the drug.
The most appropriate is matched pairs design.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Eye colors
The nominal level of measurement is most appropriate because the data cannot be ordered.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Types of movies left parenthesis drama comma comedy comma adventure comma documentary comma etc. right parenthesis
The nominal level of measurement is most appropriate because the data cannot be ordered.
Determine whether the given value is a statistic or a parameter. A study was conducted of all 2232 car owners in a certain country.
The value is a parameter because it is a numerical measurement describing some characteristic of a population.
Determine whether the source given below has the potential to create a bias in a statistical study A certain medical organization tends to oppose the use of meat and dairy products in our diets, and that organization has received hundreds of thousands of dollars in funding from an animal rights foundation.
There does appear to be a potential to create a bias. There is an incentive to produce results that are in line with the organization's creed and that of its funders.
Determine whether the study is an experiment or an observational study, and then identify a major problem with the study. In a survey, 1465 Internet users chose to respond to this question posted on a newspaper's electronic edition: "Is news online as satisfying as print and TV news?" 52% of the respondents said "yes." What is a major problem with the study?
This is an observational study because the researchers do not attempt to modify the individuals. This is a convenience sample with voluntary response, which has a high chance of leading to bias.
Refer to the definition of simple random sample available below and its accompanying definition of random sample enclosed within parentheses. Determine whether each of the following is a simple random sample and a random sample. a. A statistics class with 36 students is arranged so that there are 6 rows with 6 students in each row, and the rows are numbered from 1 through 6. A die is rolled and a sample consists of all students in the row corresponding to the outcome of the die. b. For the same class described in part (a), the 36 student names are written on 36 individual index cards. The cards are shuffled and six names are drawn from the top. c. For the same class described in part (a), the six youngest students are selected.
a. This sample is nota simple random sample. It is a random sample. b. This sample isa simple random sample. It is a random sample. c. This sample is not a simple random sample. It is nota random sample.
Determine whether the results below appear to have statistical significance, and also determine whether the results have practical significance. In a study of a weight loss program, 4 subjects lost an average of 43 lbs. It is found that there is about a 38% chance of getting such results with a diet that has no effect. Does the weight loss program have practical significance?
No, the program is not statistically significant because the results are likely to occur by chance. Yes, the program is practically significant because the amount of lost weight is large enough to be considered practically significant.
In the data table below, the x-values are the weights (in pounds) of cars and the, y-values are the corresponding highway fuel consumption amounts (in mi/gal). Weight (lb) 4073 3330 4144 3680 3571 Highway Fuel Consumption (mi/gal) 26 32 28 29 30 Comment on the source of the data if you are told that car manufacturers supplied the values. Is there an incentive for car manufacturers to report values that are not accurate?
Yes, because consumers, in general, would prefer to buy a car with a higher level of fuel efficiency. In this case, the source of the data would be suspect with a potential for bias
