2. Which of the following variables are discrete and which are continuous

1. Temperature as measured on a Celsius scale
2. Average rating from 1 to 10 of owners satisfaction with their automobile
3. The number of babies born to families
4. The speed in miles per hour of cars passing a certain point on a highway.
5. Height in inches
6. Academic rank in class

3. Scale of Measurement: Indicate the scale of measurement in the studies described below, justify your answer

1. A public opinion poll was conducted of a random sample of registered voters one week after Bush and Clinton second debate. The respondents were asked whether they intend to vote for (1) the Democratic candidate, (2) the Republican candidate, (3) the Independent candidate, (4) none of the candidates.
2. A doctor studied the physiological effects of crowding by housing laboratory rats in conditions that were crowded (10 rates per cage) or not crowded (2 rats per cage). After two months the adrenal glands of all the animals were removed and weighed to the nearest .01 gram to determine their sensitivity to stress.
3. A training officer ranked each of 20 soldiers on leadership, with the rank of 1 indicating the greatest leadership.
4. Mr. Johnson rated the 30 children in his preschool class on readiness for kindergarten by rating them on a five-point scale, 1 for least ready and 5 for most ready.
5. A college teacher gave an essay exam and then graded the paper by using five letter grades A, B, C, D, F that represented equally spaced categories of competence.
6. Students were asked whether they (1) favored an increase in the student activities fee to be eligible to attend more events, (2) favored no increase in fee to attend the current number of events, or (3) had no opinion.

Problem: From studying and compiling an extensive research literature review on domestic violence in the West Coast, you form a hypothesis that since sociability is tied very closely to verbal ability, and that sociability is a strong indicator of tolerance of ambiguity, you believe that verbal ability might be a precursor to domestic violence in the West Coast. You set out to conduct a study of volunteers from Oakland, California. You work with the Lutheran Social Services office downtown to help you recruit couples having trouble into your study and you randomly selected 20 husbands and their wives to participate. Using the Woodcock/Johnson Test of Verbal Dexterity, you measured their verbal ability on a scale of 0-100. The following are the results:

Males:

Please set up a grouped frequency distribution for each group with a class interval size (class width) of 10. Include the following in your frequency distribution: f, cf , rf , crf , and c% for both males and females. You may use SPSS and cut & paste if you like.

1. Please draw a frequency polygon for both males and females. You may use SPSS and cut & paste if you like.

3) Please state any conclusions about the shapes of the distributions.

4) Please compute the mean, median and mode for both males and females, then comment on which would best describe each set of data. Why?

Male

Mean: Median: Mode:

Best Measure: The means Why? Because the mean and the median don’t differ too significantly

Female

Mean: Median: Mode:

Best Measure: Median

5) Using the same data from the domestic violence study, please compute the standard deviation for females showing all your work.

Females:

1. Given the standard deviation for the female scores, the range of scores, and the shape of the frequency polygon, what conclusions can you draw concerning the mean?
2. Please compute the sample standard deviation (s) of the male group. No work needs to be shown for this question. You may use SPSS, EXCEL, or a Statistics calculator.

1. In the domestic violence study, one of the participants, John Davis (male), a pseudonym, scored a 72. Please compute Steve’s z -Score showing all of your work including the original formula.
   Formula: Computation:
   Z =
2. Draw a histogram with the Standard Normal Curve line for the male scores in the domestic violence study and plot where Steve Erickson’s score falls. I only need you to indicate the exact location of Steve’s score on your graph. You may use SPSS, if you like. (If you are doing this by hand you may draw only the normal curve and show Steve’s location on it). Please either way; indicate how you arrived at the location.
3. Please shade in the appropriate part of the normal curve as well. (area between z = 0 and Steve’s score).
4. What proportion of scores falls below Steve’s score?

Part 3

Suppose that teachers in Estes Park school system are given contracts of different lengths depending on such factors as years of experience, degrees held, rating at last evaluation, and field of specialty. Upon reading a report on personnel practices in Estes Park school system, you find that the distribution of lengths of teacher contracts is normal in shape, with a mean of 3 years and a standard deviation of 6 months. Given this information, comment on each of the following conclusions in terms of whether it would likely be true and why or why not. You can use numbers or percents to substantiate your answers.

1. Hardly would any teacher have a contract longer than five years.
2. Hardly would any teacher have a contract shorter than five years.
3. Great majority of teachers would have contracts with lengths between two years and four years.

1. About half the teachers would have contracts of four years or shorter.

1. Assume that the salaries of elementary school teachers in Estes Park are normally distributed with mean of $27,000 and a standard deviation of $6000. What is the cutoff salary for Estes Park teachers in the top 10%?
2. In order to help students improve their reading, Estes Park school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district, based on the scores on a reading achievement exam. If the average score for the students in the district is 122.6 with a standard deviation of 18, find the cutoff score that will make a student eligible for the program.
3. An admissions counselor states that the average cost for one year’s tuition for private high schools in the state of California is $2126. A sample of 32 high schools is selected, and the average tuition is $2159, with a standard deviation of $123. Use this information to answer the following questions:

1. What is the estimated standard error for this?
2. What is the z score for this?
3. Determine whether the above z score is significant at alpha = 0.02
4. What is the probability of committing a Type I error with this z test?

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Solution: The downloadable solution consists of 15 pages, 1570 words and 4 charts.
Deliverable: Word Document