Statistics I
if A and B are the two event of sample space S then what the following symbol signifies? Only A Only B
Either A or B or both
Either A or B Score: 10/10
Correct Solution
What are the two approach of estimate the probability of an events?
Classical and Frequency Approach Classical and Modern Approach High and low Frequency approach Nether of the above answer Score: 10/10 Correct Solution
Complete the sentence by typing your answers into the textboxes Bayes Rule: Suppose A1, A2……A A2……An n are mutually exclusive events whose union is the sample space S, i.e., one of the event must occur. If A is any event then P(Ak|A) = Score: 10/10 Correct Solution It is required to place 7 white marble and 6 black marble in a row that the black marble occupies the even places. How many possible arrangements can be made?
7!6! 3628800 Both a and b None of them Score: 10/10
Correct Solution
Among n=5 bottles coming of a filling line r1=2 have accepted fills (A) and r2=3 have nonconforming fills (N). one possible sequence or permutation for the five bottles as they are filled ANNNA. ANNNA. What is the Number of Permutation
5!/2!3! 10 Both a and b None of them Score: 10/10
Correct Solution
If we toss a coin 1000 times and find that it comes up with heads 645 times. What is the probability of a head coming up?
645/1000 0.645
6.45 0.0645 Score: 10/10
Correct Solution
If then which of the following expressions is correct?
P(A1) <= P(A2) P(A2-A1) = P(A2)-P(A1)
P(A1) = P(A2) None of the above answers Score: 10/10 Correct Solution A card is drawn at a random from an ordinary deck of 52 playing cards. Find the probability of picking a 10 or a spade 3/13
3/4 1/13
4/13 Score: 10/10
Correct Solution
Statistics II
if the x1,x2…..xn are the set of n numbers then the formula, x or µ = (X1+X2…………Xn)/n gives us, Median
Mean Variance Standard deviation Score: 10/10 Correct Solution If variance is denoted by б2 then which of the following is true for standard deviation, √б √ б^2 √2б Score: 10/10 Correct Solution
Find Find the mean and median for the set of data { 10,20,30,40,50,60,70 10,20,30,40,50,60,70} } 40, 40 40, 50 50, 50 None of above answers Score: 10/10 Correct Solution Find Find the standard deviation for the set of data { 10,20,30,40,50} 30 200 14.14 14 Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes Find the semiinterquartile range for the data set {67,69,70,71,74,77,78,82,89}
5.25 Score: 10/10
Correct Solution
Statistics III
A random variable that takes on a finite or countably infinite number of value is called…. Nondiscrete random variable
Discrete random variable
Both a and b of them None of them Score: 10/10 Correct Solution Expectation of random variable is often called mean
True
False Score: 10/10
Correct Solution
Is the expression true or false for expectation theorem (If X and Y are random variables)
E(X+Y)=E(X)E(Y) E(XY) True
False Score: 10/10
Correct Solution
Suppose that a game is to be played with a single die assumed fair. In this game a player wins 120 $ if a 3 turns up, $60 if 4 turns up and losses $30 is 5 and 6 turns up. The player neither wins nor do losses if any other face turns up. Which one of the following answer is sum of expected money? 10
20 30 40 Score: 10/10
Correct Solution
theorem of variance: if µ=E(X) then the expression for the variance is б2= E{(X- µ)2}=E(X2)- µ= E(X2)- {E(X)} 2 True
False
Score: 10/10
Correct Solution
Let X and Y be the random independent events of rolling a fair die. Compute the expected value and variance of X and Y respectively. respectively. 5.8,7
7, 5.8
7.5,8 8.5,7.8 Score: 10/10
Correct Solution
Statistics IV
A nondiscrete random Variable Variable X is said to be absolutely continuous or simple continuous, if its distribution function F() may be represented as x
F(x)=P(X≤x)= ∫f(u)du -∞
True
False Score: 10/10
Correct Solution
if x is a continuous random variable having probability density function f(x), then the variance is given by
E[(X-µ)2] Both a and b None of the Answer Score: 10/10 Correct Solution A health system analyst obtained the probability distribution for the annual number of visit by families to a clinic is as below. Number of of Vi Visit (x (x) ProbabilityP(x) 0 0.37 1 0.40 2 0.15 3 0.05 Find the expected value of o f visit by each family. family.
9.7
0.97
0.097 1 Score: 10/10
Correct Solution
Statistics V
Let ‘p’ be the probability that an event will happen in any single Bernouli trail. Then q=1-p is the probability that event will fail to happen in any single trail. The probability that the event will happen exactly x time in n trails. Then what is the probability function
P(x)= P(x)= P(x)= None of the above equation Score: 10/10 Correct Solution The special case of binomial distribution with n=1 is also called Bernouli distribution.
True False Score: 10/10
Correct Solution
What is the expression for standard deviation in binomial distribution np np(1-p)
rootnp(1-p)
All of the above answers Score: 10/10 Correct Solution Toss a fair coin 1000 times and count the number of heads that appear. What is the standard deviation of the experiments? 5 250
15.8
51 Score: 10/10
Correct Solution
What is the density function for the normal distribution? f(x)= where
f(x)=where
Both of them None of them Score: 10/10
Correct Solution
The wait X of a metal ingot producer in a smelter is normally distributed with the mean and standard deviation of X being µ=520 pounds and σ=11.What is the probability that an ingot weighting weightin g 525 pounds or less? (Use the table of cumulative probabilities and percentiles of the standard normal distribution) 0.6763
0.6736 0.3676 0.7626 Score: 10/10
Correct Solution
Suppose that the population form which samples are taken has a probability distribution with mean µ and variance σ2that is not necessarily a normal distribution.
Then the standardized variable associated associated with , given by, True False Score: 10/10 Correct Solution A team preparing a bid on an excavation project assesses that the lowest competitive bid is a continuous uniform uniform random variables X with a=$250 thousand and b=$300 thousand. Fin the probability that lowest competitive bid is between $250 thousand and $270 thousand. 0.5 0.4 0.6 4 Score: 10/10 Correct Solution
The poison probability function is f(x) = True False Score: 10/10 Correct Solution The number of crimes occurring occurring in a city district in the one hour period between 1 A.M and 2 A.M is a poisson random variables with λ=0.2. What is the probability that no crime occurs during this period. 0.8718 0.8817 0.8187 0.7818 Score: 10/10 Correct Solution The number of calls to a police dispatcher between 8:00 P.M and 8:30 pm on Friday is a poison random variable variable X with λ= 3.5. what is the probability of two or fewer fewer calls during the period 0.0302 0.1850 0.3209 0.3219 Score: 10/10 Correct Solution if n is large and if neither p or q (q=1-p) is too close to zero, the binomial distribution distribution can be closely approximated by a normal distribution with standardized random variable given by, True False Score: 10/10 Correct Solution Find the probability of getting between 3 and 6 head inclusive in 10 tosses of a fair coin by using the normal approximation to the binomial distribution. 0.7734 0.3289 0.4429 0.7718 Score: 10/10 Correct Solution What are the condition that the binomial distribution is very closely approximated by Poisson distribution
n is large and probability of occurrence of event is close to 1 n is small and probability of occurrence of event is close to 0 n is large and probability of occurrence of event is close to 1 or 0 n is large and probability p of occurrence of an event is close to 0 Score: 10/10 Correct Solution expression is true for Central limit theorem Law of large number Relation between Poisson and normal Distribution Relation between Poisson and binomial distribution Score: 10/10 Correct Solution A distance are measured as 27.3 inches and 15.6 inches with the standard deviation (error) of 0.16 inches and 0.08 inches respectively. Determine the mean and the standard deviation deviation of the sum. 42.9 inches and 0.18 inches 11.7 inches and 0.18 inches 42.9 inches and 11.7 inches None of the above answer Score: 10/10 Correct Solution Statistics VI
Complete the sentence by typing your answers into the textboxes When X is a normally distributed population, what kind population do we have? normal
population
Score: 10/10
Correct Solution
Complete the sentence by typing your answers into the textboxes The standard deviation is sometimes also called the standard error Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes Which expected value is for discrete and which for continuous distributions E(x)= E(x)= Score: 10/10 Correct Solution When X is a normally distributed population, what kind population do we have? Complete the sentence by typing your answers into the textboxes X is a random variable with E(x) = 1.5 and σ = 0.8 E(7-4X+2X^2) = 6.78 (specify with 2 digits) Score: 10/10 Correct Solution
Complete the sentence by typing your answers into the textboxes For a large value of n, the sampling distribution is very nearly a normal distribution. How large should n be? n≥ 30 Score: 10/10 Correct Solution Five hundred ball bearings have a mean weight of 5,02oz and a standard deviation of 0,30oz find the probability probability that a random sample of 100 ball bearings chose from this group will have a combined weight between 496 and 500oz. Choose one of the answers below. a = 0.2164 b = 0.3064 c = 0.4868 d = 0.2704
a b c d Score: 10/10
Correct Solution
It has been found that 2% of the tools produced by a certain machine are defective. What is the probability that defection is 3% or more in a ship of 400 such tools? Choose right solution or solutions below. a)
b)
(a) (b) (a) and (b) Score: 10/10
Correct Solution
Complete the sentence by typing your answers into the textboxes Find Find the arithmetic mean of the numbers 1, 5, 7, 8, 15, 3, 8, 4, 1, 20 Arithmetic mean = 7.2 Score: 10/10 Correct Solution (a) or (b) is called the sampling distribution of differences of the statistics.Which one? (a) = S1 – S2 (b) = µ1 - µ2 Score: 10/10 Correct Solution Statistics VII
Complete the sentence by typing your answers into the textboxes If the sampling distribution of two statistics have the same mean, the statistic with smaller variance is called a more efficient estimator of the mean. The corresponding value of the efficient statistics is then called an efficient estimate Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes If we say that a distance is 6,52 meter, we are giving a point estimate Score: 10/10 Correct Solution Under which condition can we use t-distribution?
(a) n < 30 (b) n > 30
Score: 10/10
Correct Solution
Complete the sentence by typing your answers into the textboxes A sample of five measurements of the diameter of a sphere was recorded by a scientist as 6.33, 6.37, 6.36, 6.32 and 6.37. Determine unbiased and efficient estimates the true variance. Assume that the measured diameter is normally distributed. The true variance = 0.00055 cm2 (5 digits accuracy) Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes Suppose that the heights of 100 male students at an anonym university represent a random sample of the heights of all 1546 male students at the university. university. Find a 95 % confidence intervals for estimating the mean height of the anonym university students. The true mean is 67.45 inches and the true variance is 2.93 inches. The population mean lies between 66.88 and 68.02 inches Score: 10/10 Correct Solution A simple of measurements of the diameter of a sphere gave a mean 4.38 inches and standard deviation 0.06 inch. Find 99 % confidence limits for the actual diameter. diameter. Choose one of o f the answers. (a) 4.38 + 0.00452
(b) 4.38 + 0.0650
Score: 10/10
Correct Solution
The variance for the difference of means is the same as the variance for the sum of means.
True
False Score: 10/10
Correct Solution
Statistics VIII
Complete the sentence by typing your answers into the textboxes We formulate the hypothesis that there is no difference between the two procedures. Such hypotheses are often called null hypotheses Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes Any hypothesis that differs from a given null hypothesis is called an alternative hypothesis Score: 10/10 Correct Solution Often we may be interested only in extreme values to one side of the mean, i.e., in tail of the distribution, as for example, when we are testing the hypothesis that one process is better that another. Such tests are called one-tailed tests or one-sided tests
True
False Score: 10/10
Correct Solution
Complete the sentence by typing your answers into the textboxes In most of the tests we will consider, the null hypothesis H0 will be an assertion that a population parameter has a specific value, and the alternative hypothesis H1 will be the following assertions Match right sentence with right (a) (b) (c) 1) The parameter is greater than the stated value = c 2) The parameter is less that the stated value = b 3) The parameter is either greater than or less than the stated value = a (a) two-tailed test (b) left-tailed test
(c) right-tailed test Score: 10/10 Correct Solution Scientists have two lakes who they want to compare. They have take few tests on pH-value on each lake with same method Lake 1: x1, x2, x3, x4, x5 Lake 2: y1, y2, y3, y4 (The test result is independent normal distributed random variable with µ1 for lake 1 and µ2 for lake 2, same standard deviation for lake 1 and lake 2) A confidence interval for µ1-µ2 with a confidence level of 95% is 0.40 + 0.43
True False Score: 10/10
Correct Solution
Scientists have two lakes who they want to compare. They have take few tests on pH-value on each lake with same method Lake 1: x1, x2, x3, x4, x5 Lake 2: y1, y2, y3, y4 (The test result is independent normal distributed random variable with µ1 for lake 1 and µ2 for lake 2, same standard deviation for lake 1 and lake 2) A confidence interval for µ1-µ2 with a confidence level of 95% is 0.40 + 0.43. Should we reject H0 or accept if the level of significance is 0.05? reject
accept
Score: 10/10
Correct Solution
Complete the sentence by typing your answers into the textboxes Enter question text and insert blank textbox for answer here A linear relationship exists between the variables Score: 10/10 Correct Solution Enter question text here Do these variables have any relationship between? Yes
No Score: 10/10
Correct Solution
Complete the sentence by typing your answers into the textboxes Equation y = a + bx give a straight line Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes Equation y = a + bx + cx2 c x2 give a quadratic curve Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes The process of estimation is often referred to as a regression Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes Of all curves in a given family of curves approximating a set of n data point, a curve having the property that ++….= minimum Is called a best-fitting curve in the family. Score: 10/10 Correct Solution
Complete the sentence by typing your answers into the textboxes Table below shows the respective heights x and y of a sample of 12 mother and there youngest sons. Find the least-squares regression line of y on x.
Answer: y = 35.82+ 0.48x (with 2 digits accuracy) Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes
This equation is called the standard error of estimate y on x Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes Choose the right a, b, c to the equations a) = explained variation b) = unexplained variation c) = total variation 1= c 2= b 3= a Score: 10/10 Correct Solution The linear correlation coefficient may be positive or negative. If the r is positive, y tends to ………. with x.
Increase
Decrease Score: 10/10
Correct Solution
Complete the sentence by typing your answers into the textboxes
A generalization generalization of the binomial distribution distribution id called the distribution multinomial Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes A box contains 6 blue marbles and 4 red marbles. An experiment is performed in which a marble is chosen at random and its color is observed, ob served, but the marble I not replaced. Find the probability that after 4 trials of the experiment, 4 blue marbles will have been chose. The chance is 2/7 Score: 10/10 Correct Solution
Complete the sentence by typing your answers into the textboxes 24. if the density function is
Then the distribution is
The distribution is called uniform distribution Score: 10/10 Correct Solution If the distribution is called chi-square distribution, then the ν is called Standard variance The sample variance
The number of degrees of freedom Score: 10/10 Correct Solution Complete the sentence by typing your answers into the textboxes Below is a density function to student’s distribution. When ν ≥30 , the graph of density function will closely approximates the normal curve. Score: 10/10 Correct Solution
