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12 entries in a painting competition were ranked by two judges , Judge I : 5, 2, 3, 4, 1, 6, 8, 7, 10, 9, 12, 11 and byJudge II: 4, 5, 2, 1, 6, 7, 10, 9, 11, 12, 3, 8. Calculate Spearman's rank correlation coefficient.


A manufacturer claims that only 4% of his products supplied by him are defective. A random sample of 600 products contains 36 defectives. Test the claim of the manufacturer.


A computer while calculating correlation coefficient between two variables X and Y from 25 pairs of observations obtained the following results : n=25, ∑ X= 125, ∑ X^2=650, ∑ Y=100, ∑ Y^2= 460, ∑ XY =508. If was, however, later discovered at the time of checking that he had copied down two pairs as (X,Y)= (6,14),(8,6) while the correct values were (X,Y)=(8,12),(6,8).

Obtain the correct value of correlation co-efficient.


Fit the parabola is Y=a X^2+bX+c for the data x: 1, 3, 4 , 6 ,8 ,9, 11, 14 and y: 1,2, 4, 4, 5, 7, 8, 9.


Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 97 people in the 18-21 age bracket and finds that 82 of them respond and 15 refuse to respond. When 260 people in the 22-29 age bracket are contacted, 240 respond and 20 refuse to respond. Assume that 1 of the 357 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who refused to respond.


Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.


P(22-29 or refused) =


State the null hypothesis ? and alternative hypothesis ?д for the following experiments.



2. Does fresh fruit juice have effect on colds in the group who regularly drink it compared to the group who do not?

A researcher is testing the hypothesis that all teenagers spend an average of 8 hours on their computers during the weekends. He knows that the standard deviation is 0.3 hour. He selects a sample of 144 teenagers and decides to reject the null hypothesis when the sample mean is 8.5 hours or less.



A. What us the probability of that the researcher commits a type I error?



B. If the true population mean is 7 hours, what is the probability that the he commits a type II error?



C. Determine the power of test.

new york city typically has rain on about 16% of days in October what is the probability that it will rain on exactly 5 days in October and 15 days?


On a roulette wheel, the probability of "red" is 18/38, In 10 spins what is the probability of exactly 8 red outcomes?


a)Discussthefour main types of quantitative researchdesigns


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