Exam 1: The Nature of Statistics

Identify the study as an observational study or a designed experiment. -A researcher wished to assess the importance of exercise in weight-loss programs. 412 people, all considered to be at least 20 pounds overweight, volunteered to participate in a study. The Participants were randomly assigned to one of two groups. Over a two-month period, the first Group followed a particular diet but were instructed to perform no exercise other than walking. The second group followed the same diet but also performed aerobic exercise for one hour each Day. At the end of the two months, the weight loss of each participant was recorded. The average Weight loss was calculated for each group and it was found that the average weight loss for the Second group was significantly greater than the average weight loss for the first group.

A pollster uses a computer to generate 500 random numbers and then interviews the voters corresponding to those numbers. Identify the type of sampling used in this example.

A designed experiment is described. Identify the specified element of the experiment. -A herpetologist performed a study on the effects of the body type and mating call of the male bullfrog as signals of quality to mates. Four life-sized dummies of male bullfrogs and two sound Recordings provided a tool for testing female response to the unfamiliar frogs whose bodies varied By size (large or small)and color (dark or light)and whose mating calls varied by pitch (high,Normal, or low). The female bullfrogs were observed to see whether they approached each of the Four life-sized dummies. Identify the factor(s).

Identify the study as an observational study or a designed experiment. -An educational researcher used school records to determine that, in one school district, 84% of children living in two-parent homes graduated high school while 75% of children living in Single-parent homes graduated high school.

The six members of a board of directors are Sam (S), Laurie (L), Peggy (P), Jorges (J), Max (M), and Claude (C). Consider these board members to be a population of interest. List the 15 possible Samples (without replacement)of size four from this population of six board members.

An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. Identify the sample and population.

The finalists in an essay competition are Lisa (L), Melina (M), Ben (B), Danny (D), Eric (E), and Joan (J). Consider these finalists to be a population of interest. List the 15 possible samples (without Replacement)of size two from this population of six finalists.

A newly-premiered play just ended that evening at a local theater. Theater management briefly interviews every eighth person leaving the theater to see if that person will recommend the play at That theater to other people. Identify the type of sampling used in this example.

The table below shows the total number of births in the U.S. and the birth rate per 1,000 population in each of the years 1990-1994. Year Births Birth Rate 1990 4,158,512 16.7 1991 4,110,907 16.3 1992 4,065,014 15.9 1993 4,000,240 15.5 1994 3,979,000 15.3 Classify the study as either descriptive or inferential.

A magazine publisher mails a survey to every subscriber asking about the quality of its subscription service. The total number of subscribers represents what?

The finalists in an essay competition are Lisa (L), Melina (M), Ben (B), Danny (D), Eric (E), and Joan (J). Consider these finalists to be a population of interest. The possible samples (without Replacement)of size three that can be obtained from this population of six finalists are as follows. L,M,B L,M,D L,M,E L,M,J L,B,D L,B,E L,B,J L,D,E L,D,J L,E,J M,B,D M,B,E M,B,J M,D,E M,D,J M,E,J B,D,E B,D,J B,E,J D,E,J If a simple random sampling method is used to obtain a sample of three of the finalists, what are the chances of selecting Ben, Danny, and Joan?

An education researcher randomly selects 38 schools from one school district and interviews all the teachers at each of the 38 schools. Identify the type of sampling used in this example.

A researcher randomly selects a sample of 100 students from the students enrolled at a particular college. She asks each student his age and calculates the mean age of the 100 students. It is 21.3 years. Based on this sample, she then estimates the mean age of all students enrolled at the College to be 21.3 years. In what way are descriptive statistics involved in this example? In what Way are inferential statistics involved?

Identify the study as an observational study or a designed experiment. -An examination of the medical records of 10, 000 women showed that those who were short and fair skinned had a higher risk of osteoperosis.

A college lecturer has devised a new method of teaching a particular mathematical concept and wishes to try out this teaching method on a representative sample of his students. There are 76 students in his class and he wishes to obtain a simple random sample of 25 of them. Describe a method he could use to obtain the sample.

Define the terms "stratified sampling", "systematic sampling" and "cluster sampling". Give examples for each.

A store manager wishes to deter ether his customers would be prepared to pay a little extra for organic produce. He uses a random number table to choose 50 random numbers between 1 and 200. He stands outside the store on a Monday morning between 9:00 a.m. and 12:00 noon and int e people corresponding to the random numbers. For example random number 82 would correspond to the 82nd person to arrive. Do you think that the sample obtained in this way will be representative of all the store's customers?

An education researcher was interested in examining the effect of the teaching method and the effect of the particular teacher on students' scores on a reading test. In a study, there are two Different teachers (Juliana and Felix)and three different teaching methods (method A, method B, And method C.) The number of students participating in the study is 258. Students are randomly assigned to a teaching method and teacher. Identify the treatments.

Provide an appropriate response. -Based on a random sample of 1000 people, a researcher obtained the following estimates of the percentage of people lacking health insurance in one U.S. city. Age Percentage not covered 18-24 28.2 25-39 24.9 40-54 19.1 55-65 16.5 Classify the study as either descriptive or inferential.

A mega-discount chain store just opened a new clothing store in town emphasizing mainly women's clothing. Before opening, management had to decide whether to only carry either men's, Women's, boys', girls', or infants' clothing. After performing representative sampling of potential Customers from each of these groups, it was decided to carry only women's clothing. Identify the Type of sampling used in this example.