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A relation R is defined on the set Z of all integers. In each case, prove that R is an equivalence relation. Find the distinct equivalence classes of R and list at least four members of each.
1- xRy if and only if x^2+y^2 is a multiple of 2.
Write x^2+y^2 as (x+y)^2-2xy
2- xRy if and only if x+3y is a multiple of 4.
Find the number z such that 22% of all of observations that are less than z in a standard observations from a standard normal normal distribution is 0.98.
Suppose that people's heights (in centimeters) are normally distributed, with a mean of 165 and a standard deviation of 6. We find the heights of 40 people.
Give an example of some data that you could analyze with a Chi Square. Discuss the level of measurement that you would need to use this test.
At the 5% significance level, can the researcher reject the hypothesis that the mean reading scores of all children in the three school systems is the same ? Formulate and test the appropriate hypotheses. Use the critical value approach.
Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
Start rolling dice until a particular number, say 3, is obtained, and keep track of how many rolls are necessary. Repeat 100 times. Then find the average.
A researcher has reason to believe that, for an experiment with 50 points, a 95% prediction interval would be of width 4. If the researcher wishes to run a more precise experiment that will result in a 95% prediction interval of width 2, then the ..
no children which is equal to value obtained by census. Give z statistic (rounded to two decimal places) and P-value. What do you conclude? (Use = 0.10.).
When we move from the basic normal distribution to the sampling distribution of the mean we substitute the standard error of the mean for the standard deviation when we make the conversion to the standardized normal distribution.
What is the likelihood that none of the selected flights arrived within fifteen minutes of scheduled time?
What is the appropriate procedure to test for a significant in different means between the 2 age groups. What is the p-value corresponding to your this answer and compute a 95% CI for the difference in means between the two groups.
What would you predict the price per share to be if 95 million shares were offered?
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