1. A study by a bank compared the average savings of customers who were depositors for three years or less with those who had been depositors for more than three years. The results of a sample are: less than equal to 3 years greater than 3 years Mean Savings Balance $1,200 $1,250 Population Standard deviation $100 $150 Sample Size 10 15 To test that the two groups of customers have equal savings rates, what is the p-value for a two-tailed test?
1.
A study by a bank compared the average savings of customers who were depositors for three years or less with those who had been depositors for more than three years. The results of a sample are:
less than equal to 3 years greater than 3 years
Population Standard deviation $100 $150
To test that the two groups of customers have equal savings rates, what is the p-value for a two-tailed test?
2.
A financial planner wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds, the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal.
At the 0.05 significance level, is there a difference in the mean yields of the two funds? What is the computed value of the test statistic?
3.
Identify the design of each experiment below as paired samples or independent samples. In each case give the df.
a. Ten students compared the legibility of headlines. In one condition the headlines were all in CAPITALS. In the other condition the first letters were capitalized. Each student judged on a scale of 1-10. Five judged the all capitals headline; five judged the first letter only capitalized.
b. On the basis of Critical Reading SAT scores, each male was matched with a female. Then the math SAT scores were found and the mean for the 18 males was compared to the mean of the 18 females.
c. To control for socioeconomic status, this study used only families with annual incomes in the $40-50,000 a year
d. d. A comparison of 54 fathers to their 54 sons all of whom were union members, showed the older men had higher spatial ability scores.
4.
A social psychologist wanted to determine whether attitudes of men toward abortion were different in rural and urban areas. He prepared a questionnaire and administered it to a group of city dwellers and a group of country dwellers. Each city man was matched with a country man on age, income, and education. High scores indicate positive attitudes toward abortion. Here are the questionnaire scores.
Rural Men Urban Men
22 25
19 23
18 20
17 18
15 12
10 9
6 4
4 3
a. What statistical method should be used and why?
b. Calculate a 95% confidence interval about the difference in the two populations.
c. Use the CI to test the null hypothesis that rural and urban men have identical attitudes toward abortion.
5.
Here is an experiment modeled after that of Triplett (1897), who conducted the first social psychology experiment.
Twenty-four 5th graders were given fishing reels. Twelve were tested individually. The number of yards of line reeled in 10 seconds was recorded for each. The other group was tested together under conditions of competition; the one who reeled the most line got to keep the reel. The following summary statistics were obtained.
Individuals Group Competition
EX 192 288
EX2 3347 7308
N 12 12
Analyze the results using a 99 percent confidence interval and d. with a conclusion.
1) Given Information:
A study by a bank compared the average savings of customers who were depositors for three years or less with those who had been depositors for more than three years.
Less than equal to 3 years:
Sample mean = $1,200
Population standard deviation = $100
Sample size = 10
Greater than 3 years:
Sample mean = $1,250
Population standard deviation = $150
Sample size = 15
To test that the two groups of customers have equal savings rates, what is the p-value for a two-tailed test:
State the hypothesis as follows:
Null Hypothesis or i.e., there is no significant difference between the average savings of customers. In other words, the two groups of customers have equal savings rates.
Alternative Hypothesis or i.e., the two groups of customers have unequal savings rates.
Assume Significance level
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A social psychologist wanted to determine whether attitudes of men toward abortion were different in rural and urban areas. He prepared a questionnaire and administered it to a group of city dwellers and a group of country dwellers. Each city man was matched with a country man on age, income, and education. High scores indicate positive attitudes toward abortion. Here are the questionnaire scores.
Rural Men Urban Men
22 25
19 23
18 20
17 18
15 12
10 9
6 4
4 3
a. What statistical method should be used and why?
b. Calculate a 95% confidence interval about the difference in the two populations.
c. Use the CI to test the null hypothesis that rural and urban men have identical attitudes toward abortion.
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