Statistics Chapter 1

A school psychologist wants to test the effectiveness of a new method of teaching art. She recruits 500 third​-grade students and randomly divides them into two groups. Group 1 is taught by means of the new​ method, while group 2 is taught by traditional methods. The same teacher is assigned to teach both groups. At the end of the​ year, an achievement test​ (graded on a scale from​ 1-10) is administered and the results of the two groups are compared. Complete parts​ (a) through​ (i) below. ​(a) What is the response variable in this​ experiment?

(a) What is the response variable in this​ experiment? The scores on the achievement tests of both group 1 and group 2 b. Is the response variable qualitative or​ quantitative? The response variable is quantitative because it is a measurement. (c) Which of the following explanatory variables is​ manipulated? Method of teaching ​(d) What are the​ treatments? How many treatments are​ there? The treatments are the new teaching method and the traditional teaching method. There are 2 treatments. ​(e) How are the factors that are not controlled dealt​ with? Random assignment ​(f) Which group serves as the control​ group? Group 2 serves as the control group because this group corresponds to the standard method that will be compared to the other method. (g) What type of experimental design is​ this? Completely randomized design (h) Identify the subjects. The 500 students i: Random assignment figure

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.

Why is it rare for frames to be completely​ accurate?

It is rare for frames to be accurate because frames are obtained​ periodically, whereas populations are constantly changing.

Determine the level of measurement of the variable below. Eye color

Nominal

A polling organization contacts 2511 female university graduates who have a white collar job and asks whether or not they had received a raise atnbsp work nbspduring the past 6 months.

Population in the study: Female university graduates who have a white collar job. sample in the study: The 2511 female university graduates who have a white collar job.

Define statistics.

Statistics is the science of​ collecting, organizing,​ summarizing, and analyzing information to draw a conclusion and answer questions. In​ addition, statistics is about providing a measure of confidence in any conclusions.

Sixty patients with vision loss are divided into two groups. One group is treated with experimental surgery. The other is not. After one month​, both groups are questioned about their ability to read.

The study is an experiment because the researchers control one variable to determine the effect on the response variable.

Determine whether the quantitative variable is discrete or continuous.

The variable is continuous because it is not countable.

The data on the right relate to characteristics of​ high-definition televisions A through E.

What are the individuals being​ studied? The​ high-definition television setups A through E. What are the variables and their corresponding data being​ studied? Size ​(40​, 46​, 57​, 60​, 54​), screen type ​(Plasma​, Plasma​, Projection​, Projection comma Plasma​), and number of channels available ​(300​, 113​, 423​, 270​, 290​) Determine whether each variable is​ qualitative, continuous, or discrete. Size is a continuous variable. screen type is is a qualitative variable number of channels available is a discrete variable

Researchers wish to know if there is a link between hypertension​ (high blood​ pressure) and consumption of salt. Past studies have indicated that the consumption of vegetables offsets the negative impact of salt consumption. It is also known that there is quite a bit of​ person-to-person variability as far as the ability of the body to process and eliminate salt. ​However, no method exists for identifying individuals who have a higher ability to process salt. It is recommended that daily intake of salt should not exceed 2500 milligrams​ (mg). The researchers want to keep the design​ simple, so they choose to conduct their study using a completely randomized design. Complete parts​ (a) through​ (c).

a. Blood pressure b. Body's ability to process salt, Daily consumption of salt, Daily consumption of vegetables c. blood pressure is not a factor daily consumption of salt can be controlled body's ability to process salt cannot be controlled age is not a factor gender is not a factor Experimental units should be randomized to each treatment group.

Suppose you are the president of the student government. You wish to conduct a survey to determine the student​ body's opinion regarding student services. The administration provides you with a list of the names and phone numbers of the 662 registered students. ​(a) Discuss a procedure you could follow to obtain a simple random sample of 5 students. ​(b) Obtain this sample. LOADING... Click the icon to view the portion of the random number table.

a. List each name on a separate piece of​ paper; place them all in a​ hat, and pick five. b. Number the names from 1 to 662 and use a random number table to produce 5 different​ three-digit numbers corresponding to the names selected. c. 243, 269, 250, 638, 111

The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 5588 employees at the company and wants to conduct a systematic sample of size 60.

k=93

Researchers wanted to determine if there was an association between daily apple consumption and the occurrence of high cholesterol. The researchers looked at 93 comma 715 women and asked them to report their apple​-eating habits. The researchers also determined which of the women had high cholesterol. After their​ analysis, the researchers concluded that consumption of two or more servings of Granny Smith apples per day was associated with a reduction in high cholesterol. Complete parts​ (a) through​ (c) below.

​(a) What type of observational study was​ this? Explain. This was a​ cross-sectional study because all information about the individuals was collected at a specific point in time. b) What is the response variable in the​ study? Is the response variable qualitative or​ quantitative? What is the explanatory​ variable? The response variable is whether the woman has high cholesterol or not. The response variable is qualitative. What is the explanatory​ variable? The explanatory variable is consumption of Granny Smith apples. ​(c) In their​ report, the researchers stated that​ "After adjusting for various demographic and lifestyle​ variables, daily consumption of two or more servings was associated with a​ 30% reduced prevalence of high cholesterol​." Why was it important to adjust for these​ variables? The researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when there are some explanatory variables that were not considered in a​ study, but that affect the value of the response variable.