Assignment 10 Questions.
1. Statistics indicates that the average female literacy rate for 109 countries of the world was 67.3 percent in 1995, with a standard deviation of 28.6. The average male literacy rate for the world was 78.7%, with a standard deviation of 20.4.
a) The female literacy rate in Nicaragua was 57%. The literacy rate for males was also 57%. On which indicator did the country have a relatively lower score than the world in general?
b) knowing that the average literacy rate for females in the world was 67.3 percent, with a standard deviation of 28.6, we can expect three quarters of female literacy rates for all countries to fall within which values on both sides of the mean?
c) The z-score for the female literacy rate in Ukraine was 1.14. What was its original score on female literacy rate, in percentages?
2. The question on whether the people will agree to rise taxes in order to prevent damage to the environment was asked in the World Value Survey. For Canada and the US, the results of the survey were as follows:
Support Higher Taxes to help the environment? Canada US
Yes 818 1616
No 429 1028
a). What is the percentage of those in favour of rising taxes out of the total?
b) Can we claim that support for increasing taxes in order to save the environment is higher in Canada than the US? Calculate and compare the column percentages to support your conclusion.
c) Based on the method of maximum difference, what conclusion can you make about the difference between the support for increasing taxes for environment in Canada and the US?
d) Draw two bar graphs showing the relative support and disapproval for rising taxes for environment in both Canada and the US, side by side. The vertical axes should show the percentage of people who are in favour or against raising taxes.
3. SPSS question. Are females in the US more traditional in their sexual behaviour than males? The GSS survey in 2002 asked respondents to express their opinion on sexual relationship before marriage. Using the data file for 2002, compare the opinion of females and males on the issue.
a) In a paragraph, present and discuss the appropriate crosstab of opinions on premarital sexual relationships by gender. Produce the table in SPSS and include appropriate percentages for comparison of opinion of two gender groups. Justify your choice of percentages (total, column, or row).
b) present and discuss an appropriate graph, comparing the distribution of percentages in the two groups on the issue. Justify your choice of the graph.
4. H11.4: Many analysts have noted a "gender gap" in elections for the U.S. presidency with women more likely to vote for the Democratic candidate. A sample of university faculty has been asked about their political party preference.
Party Preference Male Female Totals
Democratic 10 15 25
Republican 15 10 25
Totals 25 25 50
a) calculate the chi-square for gender and party preference. b) compute column percentages for the table to determine the pattern of relationship. Which gender is more likely to prefer the Democrats?
5. H13.4. The director of a shelter for battered women has noticed that many of the women who are referred to the shelter eventually return to the violent husbands even when there is every indication that the husband will continue the pattern of abuse. The director suspects that the women who return to their husbands do so because they have no place else to go- for example, no close relatives in the area with whom the women could reside. Do the data below support the director's suspicions? Calculate two appropriate statistical measures to support your conclusion.
Return to Husband? Yes No Totals
Yes 10 23 33
No 50 17 67
Totals 60 40 100
6. H 13.10 a). A sociologist is researching public attitudes toward crime and has asked a sample of residents of his city if they think that the crime rate in their neighbourhoods is rising. Is there a relationship between sex and perception of crime rate? Write a paragraph summarizing the information presented in these tables, and calculate two appropriate measures to indicate whether the relationship exists.
Perception of crime rate by sex:
Crime Rate is Male Female Totals
Rising 200 225 425
Stable 175 150 325
Falling 125 125 250
Totals 500 500 1000
7. A sample of children has been observed and rated for the symbols of depression. Their parents have been rated for authoritarianism. Is there a relationship between these two variables? Compute the appropriate measure of association and interpret it. Justify your choice of statistics.
Depression Low High
Few 9 7
Many 3 10
8. H14.12. Several years ago, a job-training program began, and a team of social workers screened the candidates for suitability for employment. Now the screening process is being evaluated, and the actual work performance of a sample of hired candidates has been rated. Did the screening process work? Is there a relationship between the original scores and performance evaluation on the job? Treat original scores and performance evaluation as ordinal variables with many categories. Calculate and discuss the appropriate statistics, justifying its choice.
Case Original Score Performance Evaluation
A 17 78
B 17 85
C 15 82
D 13 92
E 13 75
F 13 72
G 11 70
H 10 75
I 10 92
J 10 70
K 9 32
L 8 55
M 7 21
N 5 45
O 2 25
9. Research suggests that there is a strong negative correlation between satisfaction with work scores and propensity to leave a job. Suppose an assessment was done for a group of workers, comparing their work satisfaction, x, and propensity to leave a job, y. The assessment produced the following scores on interval-ratio scale:
X 12 24 17 28 24 36 20
Y 44 36 25 23 32 17 24
a. Find the linear correlation between x and y.
b. What does the value of this correlation coefficient tell us? Explain.
10. H.15.2 Occupational prestige scores for a sample of fathers and their oldest son and oldest daughter are shown in the table.
Family Father's Prestige Daughter's Prestige
A 80 82
B 78 77
C 75 68
D 70 77
E 69 60
F 66 52
G 64 48
H 52 57
For father's and daughter's prestige only, do the following:
a) Draw a scattergram, and a freehand regression line.
b) Compute the slope and the intercept. Interpret them. Add the real regression line to the graph above.
c) State the least-squares regression line. What prestige score would you predict for a daughter whose father had a prestige score of 72? Of 54?
d) calculate and interpret r and r2. .
This solution gives the step by step method for analysis GSS data in spss.
Analysis of GSS data in SPSS
1. The speed of an airplane in miles per hour is a ___________________ variable.
2. A football team's rank is a ___________________________variable.
3. The __________________ for a set of data is found by adding all the data values and dividing by the number of items.
4. The range or the ______________________________ can be used for measuring the variability of ordinal variables.
5. The mode is the only measure of central tendency for _____________________ data.
6. A ____________________ variable affects a ____________________.
7. The ____________________measures the variability of the dependent variable based on the variability of the independent variable.
8. A _______________________________is a graphical representation for analyzing the relationship between categorical variables.
9. A _____________________________ is a graphical representation for analyzing the relationship between numerical variables.
10. When we are looking at the association between an independent variable and a dependent variable we are doing a _________________.
11. The measure of association for numerical variables is ______________________________.
12. The two measures of association most commonly used for ordinal variables are _____________________and ______________________.
13. For the Chi-squared Test for Independence the ___________________ states that there is an association between the two variables.
14. The error that may occur by rejecting the null hypothesis is called ___________________________.
15. The error that may occur by accepting the null hypothesis is called _______________________________.
16. The likelihood that a test statistic of a particular magnitude computed from a sample is indicated by the ______________________.
17. A hypothetical distribution of the characteristics of all possible samples of a certain size drawn from a population is the ___________________________________.
18. The standard deviation of the sampling distribution of the sample means is the _______________________________.
19. A theory about the sampling distribution which tells us that the larger the size of the sample from a population is the more likely it is that the mean of a single sample will be close to the mean of the population is called the ____________________________________.
20. ________________________________ are numbers that help us assess the likelihood that patterns we observe in randomly drawn samples will be found in the populations from which those samples were drawn.
Part II: Short Answers
1) A random sample of 81 automobile tires has a mean tread life of 36,000 miles. It is known that the standard deviation of the tread life of the tires is 4500 miles.
a. A 95% confidence interval for the population mean is:
b. If the sample mean of 36,000 had been from a random sample of size 50, the 95% confidence interval would have been (pick one of the below statements)
i. The same
ii. A wider interval
iii. A narrower interval
2) Consider the following two-tailed test:
Assume that and that a sample of size 100 resulted in a sample mean of .
a) What is the value of the test statistic?
b) At the 0.05 level of significance, what conclusion should be reached?
3) An accountant believes that the company's cash flow problems are a direct result of the slow collection of accounts receivable. The accountant claims that at least 70% of the current accounts receivable are over 2 months old. A sample of 120 accounts receivable yielded 78 over 2 months old.
a) What is the value of the test statistic?
a) At the 0.05 level of significance, is the accountant correct?
4) Use the following for questions. A testing company is checking to see if there is any significant difference in the coverage of two different brands of paint for a hardware store chain. The results are summarized below.
Amazon Paints Cover up Paint
Mean coverage (in square feet) 305 295
Standard Deviation 20 25
Sample size 31 41
a) A point estimate of the difference between the population mean is
b) A estimate of the standard error of the difference between the sample means is
c) If a two-tailed test is used with a 0.05 level of significance, what conclusion would the testing company make if they thought that there was no difference in the mean coverage of the two paints?
5) Analyzing SAT Scores: The College of Newport randomly selects female applicants for admission and records their scores on the math portion of the SAT. Here are the results:
490, 570, 630, 440, 460, 720, 410, 780
a. Find the mean of this sample.
b. Find the standard deviation.
c. Using a 0.05 significance level to test the claim that this sample comes from a population with a mean equal to 496, which is the reported mean of SAT math scores for all women.
Part 3: Answer the following questions using SPSS and the GSS data (GSS 2002 subset C - Attached).
1. Researchers say that there is a relationship between how fundamental one is and their views on whether birth control pills should be given to teenagers. To test this GSS survey asked respondents how fundamental they are in their views and whether giving birth control pills are okay to teenagers. Write a few sentences analyzing the relationship between pillok and fund using the appropriate measure of association.
2. Researchers believe that people who go to church tend to be happier in general. Test to see if there is an association between rcattend and happy using the Chi-Squared Test of Independence.
3. In the past, the average household had 2.5 children. Use the one-sample t-test to determine if that is true using the variable rchilds.View Full Posting Details