Search & Filtering
A researcher claims that 75% of college students would rather spend their money for mobile phone loads than cigarettes. Another researcher would like to verify this claim. She randomly selected 400 college students. Two hundred ninety-six of these 400 students said that they would rather spend their extra money on mobile phone loads than cigarettes. At 0.05 level of confidence, is there enough evidence to conclude that the percentage of students who would rather spend their extra money for mobile phone loads than cigarettes is different from 75%.
A research conducted on a certain company last year showed that 25% of the employees would rather drink coffee than soft drinks during break time. The company has recently decided to give free coffee during break time. In the new research conducted this year, out of the 125 randomly sampled employees 28% said that they would rather drink coffee than soft drinks. At 0.05 level of significance, is there sufficient evidence to suggest that the coffee drinkers have increased since the company has decided to give free coffee during break time?
Only 30% of students consider statistics to be an exciting subject. Find the probability that I must ask more than 5 students before I get one who consider statistics to be an exciting subject.
.0720
.1681
.8319
.9280
Suppose the set of possible values for (X, Y ) is the rectangle D = {(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}. Let the joint probability density function of (X, Y ) be f(x, y) = 6 5 (x + y 2 ), for (x, y) ∈ D. a) Verify that f(x, y) is a valid probability density function b) Find P(0 ≤ X ≤ 1/4, 0 ≤ Y ≤ 1/4). c) Find the marginal pdf of X and Y. d) Find P(1/ 4 ≤ Y ≤ 3 /4 )
A fair coin is tossed three times independently: let X denote the number of heads
on the first toss and Y denote the total number of heads. Find the joint probability
mass function of X and Y .
a) Provide the joint distribution table of the above experiment.
b) Find the
i) the marginal probabilities of X and Y
ii) P(X<Y)
Make a study about how many sheets of paper you consumed weekly in
answering your Self Learning Modules. Record the quantity (total number of sheets)
per subject, then construct a probability distribution. Compute the mean, variance,
and the standard deviation of the probability distribution you made. Interpret the
result, then find out how many weeks you will consume 50 sheets of pad paper.
The random variable Y has the distribution function
F(y)= 0 y<1
ln 0<y<1
1y>1
find the following, i) P( y>2) ii) P(2<y<2)
A psychologist who is conducting learning experiments with rats has prepared a simple web with just two narrow paths through it. When the rat is introduced into the web, it must go down one of the paths. One leads to food, the other does not. Each rat is introduced to the same web three times, and an outcome on each trial is noted. (i) Give a suitable sample space for this experiment. (ii) Let the random variable X be the number of times the rat succeeds in reaching the food. Give the distribution table for the realizations of X. and (iii) Find the Cumulative distribution function (cdf) for X. (iv) Graph the The pdf and cdf for random variable x, the number of times the rat succeeds in reaching the food
The number of accidents in a highway as recorded every month over a 9 month period are 15,18,9,11,14,10,8,13,19. Test at 5% frequencies are in in agreement with the belief that the number of accidents was the same during the 9 months. it is given that the table values of x² at 5% level for 8 d.o.f. are 15.5 and 16.9 respectively.
How much does ten pounds of weight change the estimated number of cups of dog
food consumed? Dog 1 2 3 4 5 6 7 8 9
Weight 0.41 1.48 0.79 0.41 0.85 1.11 0.37 1.11 0.41
Consumption in cups 3 8 5 4 5 6 3 6 3
Dog 10 11 12 13 14 15 16 17 18
Weight 0.91 1.09 2.07 0.49 1.13 0.84 0.95 0.57 1.68
Consumption in cups 5 6 10 3 6 5 5 4 9
Dog 1 2 3 4 5 6 7 8 9
Weight 0.41 1.48 0.79 0.41 0.85 1.11 0.37 1.11 0.41
Consumption in cups 3 8 5 4 5 6 3 6 3
Dog 10 11 12 13 14 15 16 17 18
Weight 0.91 1.09 2.07 0.49 1.13 0.84 0.95 0.57 1.68
Consumption in cups 5 6 10 3 6 5 5 4 9
