BackSampling Method Assume that the population consists of all students currently in your statistics class. Describe how to obtain a sample of six students so that the result is a sample of the given type.
c. Stratified sample
In Exercises 5–12, identify whether the given value is a statistic or a parameter.
Drivers According to the Federal Highway Administration, there are 212 million licensed drivers in the United States.
Sampling Method Assume that the population consists of all students currently in your statistics class. Describe how to obtain a sample of six students so that the result is a sample of the given type.
a. Simple random sample
Define the following: Placebo
Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.
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Fixed Percentage If a restaurant were to change its tipping policy so that a constant tip of 20% of the bill is added to the cost of the dinner, what would be the value of the linear correlation coefficient for the paired amounts of dinners/tips?
In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.
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Is the process mean within statistical control? Why or why not?
Daily Coffee Consumption Is there an association between daily coffee consumption and the occurrence of skin cancer? Researchers asked 93,676 women to disclose their coffee-drinking habits and also determined which of the women had nonmelanoma skin cancer. The researchers concluded that consumption of six or more cups of caffeinated coffee per day was associated with a reduction in nonmelanoma skin cancer. Source: European Journal of Cancer Prevention, 16(5): 446–452, October 2007.
What is the response variable in the study? What is the explanatory variable?
"In Problems 3–10, determine whether the underlined value is a parameter or a statistic.
School Bullies In a national survey of 1300 high school students (grades 9 to 12), 32% of respondents reported that someone had bullied them at school. Source: Bureau of Justice Statistics"
Platelet-Rich Plasma Does a platelet-rich plasma (PRP) injection into the scalp promote hair growth? Researchers identified 30 female patients with female pattern hair loss. The patients ranged in age from 20 to 45 years. For each patient, two areas with hair loss were identified. A coin toss was used to decide which area received the PRP injection and which received a saline injection. Injections were given to each patient at one-week intervals. After 6 months the change in the patients’ hair density (number of hairs per square centimeter) and hair diameter (millimeters) was measured. The mean difference in hair density (PCP minus saline) was 59.47 hairs/cm2 and the mean difference in hair thickness was 0.08 mm.
What is the population that is being studied?
In Exercises 13–20, determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.
Election Fraud The County Clerk in Essex County, New Jersey, was responsible for randomly assigning the order in which candidates’ names appeared on a recent election ballot. Among 41 different ballots, a Democrat was placed on the first line 40 times, and a Republican was placed on the first line once.
A report shows the amount (in dollars) spent by each customer in a grocery store. Is this data set a population or sample?
"Insurance and Credit Scores A study by InsuranceQuotes.com found that homeowners with poor credit pay 91% more for home insurance than people with excellent credit.
a. A quote in the article stated, “Insurers have found a direct correlation between a consumer’s credit and the likelihood that he or she will make a home (or auto) claim.” Explain what is wrong with this quote."
Computer Virus In an AOL survey of Internet users, this question was posted online: “Have you ever been hit by a computer virus?” Among the 170,063 responses, 63% answered “yes.” What term is used to describe this type of survey in which the people surveyed consist of those who chose to respond? What is wrong with this type of sampling method?
Retain Your Knowledge: Decision Making and Hunger Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 normal weight individuals into two groups. All subjects were asked to refrain from eating or drinking (except water) from 11 P.M. on the day prior to their 9 A.M. meeting. At 9 A.M., the subjects were randomly assigned to one of two groups. The subjects in Group 1 were fed breakfast while the subjects in Group 2 were not fed. All subjects were administered a computerized version of an exam that assesses complex decision making under uncertain conditions. The assessment consisted of subjects choosing cards from four decks marked A, B, C, and D. Cards in decks A and B had a point value of 100 while cards in decks C and D had point values of 50. However, deck A had penalty cards that deducted points between 150 and 300; deck B had one penalty card of 1250; deck C had penalty cards between 25 and 75 points; deck D had a single penalty card of 250 points. So, decks A and B had stiffer penalties over the long haul than decks C and D and in the long haul, decks C and D resolted in more points than decks A and B. In total, the subjects would select 100 cards. However, the response variable was the number of cards selected from decks C and D out of the last 60 cards selected. The thinking here is that after 40 card selections, the subjects would be aware of the advantage of decks C and D. The researchers administered a Barret Impulsivity Scale to be sure the two groups did not differ in terms of impolsivity (e.g., “I do things without thinking”). There was no difference in impulsivity, age, or body mass index between the two groups. Before the exam, subjects were asked to report their level of hunger and it was found that Group 2 was significantly more hungry than Group 1. After analysis of the data, it was determined that the mean number of advantageous cards (decks C and D) selected by the subjects in Group 2 was 33.36 cards while the mean was 25.86 for the subjects in Group 1. The researchers concluded that hunger improves advantageous decision making.
g. What is the conclusion of the study?
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning.
In January 2021, 54% of the governors of the 50 states in the United States were Republicans. (Source: National Governors Association)