Solved: Two samples consisting of 21 and 9 observations have variances given by s 1 2 =16 and s 2 2 =8 respectively. Test the hypothesis that the first population variance is greater than the second at a (a) 0.05, (b) 0.01 level of significance.

Let X be a random variable that denotes the number of passengers in a train station for a given hour. What are the possible values of X?

Find the mean of the probability distribution of the random variable X, which can take only the values 2,3,4,5 given that p(2)= 2/7, P(3)= 3/7, P(4) = 1/7, and P(5)= 1/7.

For each of the following scenarios, give an example of a discrete and a continuous random variable. The first one is done as an example. Scenarios •Asking your classmates about their breakfast. •M…

Let X be a discrete random variable such that X = 0 with probability 0.5 and X = 1 with probability 0.5. Let Y be a discrete random variable such that Y = 0 when X = 1 and Y = 1 when X = 0. What is the mean and variance of X + Y?

A box contains 5 green and 2 blue dice.Four dice are chosen one after the other .Determine the values of the random variable G representing the number of green dice.

4. A soft-drink machine is regulated so that it discharges an average of 200 mls per cup. If the amount of drink is normally distributed with a standard deviation equal to 15 mls. Below what value do we get the smallest 30% of the cup…

a taxi cab company has 12 ambassadors and 8 fiats. If 5 of these taxi cabs are in workshop for repair, calculate the probability that i) 3 of them are ambassadors and 2 flats ii) all the 5 are of the same make

1 4 4 2 3 4 5 1 4 1 Work out the mode

A spinner for a child's game has the numbers 1 through 9 evenly spaced. If a child spins, find each probability: a. The number is divisible by 3.

Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in ev…

Regression of yi = ꞵ0 + ꞵ1 xi1 + ꞵ2 xi2 + ꞵ3 xi3 + ꞵ4 xi4 + ui yields the following results in tabular form. The tabulated t- statistics is 2.6 , 1.96 and 1.64 for one , five and ten percent significance levels respectively. State the…

A spinner for a child's game has the numbers 1 through 9 evenly spaced. If a child spins, find each probability: a. The number is divisible by 3. b. the number is greater than 7. c. The number is an even number.

a) Consider the following functional relation, f, defined as: f : R \rightarrow R, f(x) = x2 Determine whether or not f is a bijection. If it is, prove it. If it is not, show why it is not. b) Consider the set F = {y | y = a…

Consider the lot of fluorescent tubes in number 100.if 50 samples of 100 tubes are drawn from the lot with replacement find the expected number of sample will have mean life atleast 1600 hrs. Flourescent tubes are 1570 hrs with a s.d.…

A recent survey found that 54.7% of the population own their homes. In a random sample of 150 heads of households, 92 responded that they owned their homes. At 0.01 level of significance does that indicate a difference from the nation…

Researcher is using data for a sample of 10 observations to estimate the relation between consumption expenditure and income. Preliminary analysis of the sample data produces the following data. ∑xy = 700 , 1000 2 ∑x = , ∑X = 1…

A report stated that the average age of commercial jets in country X is 14 years. An executive of a large airline company selects a sample of 36 planes and finds that the average age of the plane is 11.8 years. The standard deviation …

The odds of Matthew doing his math homework is 13:7. What is the probability of Matthew doing his homework once in the next two days?

Using the data given below, calculate the 3 and 5 years moving averages. Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Sales 2354 2380 2319 2469 …

let x be a random variable with probability density function given by f(x)=(2he^-1/4x ; 0

A politician believes that 25% of all macroeconomists in senior positions would strongly support a proposal he wishes to advance. Suppose that this belief is correct and that five senior macroeconomists are approached at random. What …

FIND THE VALUES FOR EACH OF THE FF. CASES: A. UPPER TAIL AREA OF 0.025 WITH DEGREE OF FREEDOM=28 B. LOWER TAIL AREA OF 0.01WITH DEGREE OF FREEDOM=15 C. WHERE 90% OF THE AREA FALLS BETWEEN THESE TWO t-VALUES WITH df=9

the number of defective production in a production process follows a poisson distribution with a mean of 2.6 per month, for a given month what is the probability there will be fewer than two defective production?

According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3388…

The owner of a factory that sells a particular bottled fruit juice claims that the average capacity of their product is 250 ml. To test the claim, a consumer group gets a sample of 100 such bottles, calculates the capacity of each bot…

According to the article "A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" published in the Journal of the American Medical Associ…

A factory manufacturing light-emitting diode (LED) bulbs claims that their light bulb last for 50 000 hours on the average. To confirm its this claim is valid, a quality control manager got a sample of 50 LED bulbs and obtained a life…

A box contains 18 light bulbs. Of these, four are defective. Five bulbs are chosen at random. What is the probability that four are defectives?

what happens to the variance of the sampling distribution of the sample means when the sample size increases

Determine if the following are probability distributions (if no, state why) x= {3,6,9,12,15} p(x)= {4/9,2/9,1/9,1/9,1/9}

The following represent the scores of a group of students on two tests. calculate spearman rs and kendall's tau for these data. Test 1 - 36, 34, 33, 29, 29, 28, 28, 28, 24, 22, 19, 12 Test 2 - 18, 26, 24, 18, 15, 12, 14, 13, 12, 10,…

1. To the left of z= -1.66 2.to the left of z=1.47 3.to the right of z=2.52 4.to the right of z= -1.75 5.between z=1.5 and 2.76

The following represent the scores of a group of students on two tests. calculate spearman rs and kendall's tau for these data. Test 1 - 36, 34, 33, 29, 29, 28, 28, 28, 24, 22, 19, 12 and Test 2 - 18, 26, 24, 18, 15, 12, 14, 13, 12, 1…

Three judges rated eight essays with the following results. Calculate the coefficient of concordance with these data. JUDGE ESSAY 1 2 3 1 8 7 8 2 6 5 6 3 4 6 5 4 1 2 1 5 3 3 2 6 2 1 3 7 5 4 4 8 7 8 7

The following data represent the operating time in hours for 4 types of pocket calculators before a recharge is required. Use the Kruskal-Wallis test, at the 0.01 level of significance, test the hypothesis that the operating times for…

Two coins are tossed. Let H be the number of tails that occur. Determine the values of the random variable H.

The mean annual cost of car insurance is Rs 9450 and standard deviation of Rs 250. What is the probability that the average insurance cost of a sample of 25 cars will be between Rs 9400 and Rs 9500?

box a and box b contains 1,2,3,4. write the probability mass function and draw the histogram of the sum when one number from each box is taken at a time, with replacement

it is reported that 72% of the working women use computers at work. Choose 5 women at random and find the probability that at least 1 doesn't use a computer at work

determine if the following are probability distribution (if no, state why) X=1,2,3,4 and 5 P(x)= 3/10, 1/10, 1/10, 2/10 and 3/10

Construct a probability distribution of the random variable X for the number of false answers in a 4-item true or false test.

Construct probability distribution for the random variable X on the number of defective units selected when five units are chosen at random from a batch of ten flash drives which contains four defective items.

The water bills for residents in Davao City have a mean of Php2085 and a standard deviation of Php129. Random samples of 86 water bills are drawn from this population, and the mean of each sample is determined. What is the mean of the…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 655 hours and a standard deviation of 21 hours. Random samples of 43 bulbs are drawn from this popul…

Find the proportion area of the region between z= -2 and z= -3

Population 1 consists of the values 5, 7, and 9. Population 2 consists of values (1, 5). Consider all the possible samples of size 2 that can be drawn with replacement from population 1 and all the possible samples of size 3 that can …

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 786 hours and a standard deviation of 80 hours. Find the probability that a random samples of 17 bul…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 616 hours and a standard deviation of 54 hours. Random samples of 31 bulbs are drawn from this popul…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 796 hours and a standard deviation of 55 hours. Find the probability that a random samples of 40 bul…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 806 hours and a standard deviation of 90 hours. Find the probability that a random samples of 15 bul…

Let x denote the number of biased die with the following probability mass function p(x) X: 1 2 3 4 5 6 P(x): 1/6 1/6 1/5 y 1/5 1/6 a) find the value of y

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 780 hours and a standard deviation of 89 hours. Find the probability that a random samples of 31 bul…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 798 hours and a standard deviation of 80 hours. Find the probability that a random samples of 39 bul…

Let x denote the number of biased die with the following probability mass function p(x) X: 1 2 3 4 5 6 P(x): 1/6 1/6 1/5 y 1/5 1/6 a) find the value of y b) find the cdf of x

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 810 hours and a standard deviation of 92 hours. Find the probability that a random samples of 39 bul…

a) Marks out of 100 for 100 students were tabulated as shown below: Marks f 11 – 20 4 21 – 30 16 31 – 40 27 41 – 50 32 51 – 60 15 61 – 70 4 71 – 80 2 i) Calculate the mean mark. (4 ma…

a presidential candidate asks a polling to conduct a nationwide survey to determine the percentage of potential voters who would vote for him over his rival presidential candidate. out of 2 500 respondents in the sample, 945 said they…

X: the number of automobile accidents per year in Virginia.

An overseas shipment of 5 foreign automobiles contains 2 that have slight paint blemishes. If an agency receives 3 of these automobiles at random, list the elements of the sample space S, using the letters B and N for blemished and no…

Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of …

In a National Achievement Test, suppose three test booklets are tested at random. Let D represent the defective test booklet and let N represent the non-defective test booklet. Let X be the random variable representing the number …

In a survey, 1087 randomly selected adults were asked "Do you have occasion to use alcoholic beverages such as liquor, wine, or beer, or are you a total abstainer?" 62% of the subjects said that they used alcoholic beverages…

Two balls are drawn in succession without replacement of an containing 5 white balls and 6 black balls Let B be the random variable representing the number of black balls. Construct the probability distribution of the random variable R

The recommended retail price of a brand of designer jeans is known. The price of the jeans in a sample of 16 retailers is on average $141 with a sample standard deviation of 4. If this is a ‘random’ sample and the prices can be assume…

In a normal distribution, if the mean score is 8 in a gymnastics competition and the student scores a 9.3, what is the z-score if the standard deviation is 2.5?

In a wage discrimination case involving male and female employees, it is assumed that male employees have a mean salary equal to that of female employees. To justify this, independent random samples of male and female employees were t…

There is a bag filled with 3 blue,2 red and 4 green marbles.A marble is taken at random from the bag,the colour is noted and then replaced.Another marble is taken at random.What is the probability of getting 2 different colours?

A cigarette manufacturer wishes to test the claim that the variance of the nicotine content of its cigarettes is 0.644. Nicotine content is measured in milligrams and assume that it is normally distributed. A sample of 2…

Two groups of children were given visual acity tests-group. group 1 was composed of 11 children who receive their health care from private physician. the mean score for this group was 26 with standard deviation of 5.group 2 was compos…

Zaheeda scored 9 goals in 5 netball matches At this rate about how many goals will she score in 10 games

Let the random variable XX be the random of the amount won. The random variable XX may take on only two value, (0,3000). That is x=0,3000x=0,3000 There are five hundred tickets to be sold and only one ticket wins P3,000. Therefore,…

1. For each of the following, determine whether it can serve as the probability distribution of some random variable: a) p(k) = 1/7 , for k = 0; 1; 2; 3; 4; 5; b) p(x) = x2 /30 , for x = 0; 1; 2; 3; 4; c) p(y) = (y+4)/(y-4) , for y…

Five hundred tickets will be sold, and these will be raffled during the town fiesta. One of these tickets will win P3,000, and the rest will win nothing. What will be the expected outcome and variance of your gain if you buy one of th…

Refer to Exercise 5. What is the expected number of patients with undesirable side effects. What is the standard deviation of the number of patients with undesirable side effects.

A doctor knows from experience that 10% of of the patients to whom he prescribes a certain blood pressure medication will have undesirable side effects. Calculate the probability that of the 10 randomly selected patients: a) none …

Explain in each case why the given equation cannot serve as the probability density function of a random variable that takes on values on the interval from 0 to 5: a) f(x) = 1/10 (x - 4); b) f(x) = 1/50 (x + 1).

Five hundred tickets will be sold, and these will be raffled during the town fiesta. One of these tickets will win P3,000, and the rest will win nothing. What will be the expected outcome and variance of your gain if you buy one of th…

In a certain village 28% of all cars are made by Ford. (ii) 14 cars are chosen randomly in this village. Find the probability that fewer than 4 of these cars are made by Ford. (iii) A random sample of 50 cars in the village is taken…

A frozen food distributor claims that 80% of its frozen chicken dinners contain at least three ounces of chicken. To check the claim, a consumer testing service decides to check ten of these chicken dinners and rejects the claim unles…

8. A quality control engineer wants to check whether, in accordance with speci cation, 90% of products shipped are in perfect working condition. To this end, she randomly selects 12 items from each lot ready to be shipped and passes t…

In a certain village 28% of all cars are made by Ford. (ii) 14 cars are chosen randomly in this village. Find the probability that fewer than 4 of these cars are made by Ford. (iii) A random sample of 50 cars in the village is taken…

Find z if the standard normal-curve area a) between 0 and z is 0.4726; b) to the left of z is 0.9868; c) to the left of z is 0.3085; d) between -z and z is 0.9282 12. If a random variable has the normal distribution with \…

A certain type of ochro seed germinates 75% of the time. A backyard farmer planted 6 seeds. What is the probability that more than 4 seeds germinate?

The grapefruits grown in a large orchard have a mean weight of 18.2 ounces with a standard deviation of 1.2 ounces. weights of these grapefruits has roughly the shape of a normal distribution, what percentage of the grapefruit weigh …

18. The lengths of fully-grown scorpions of a certain variety have a mean of 1.96 inches and standard deviation of 0.08 inch. Assuming that the distribution of these lengths has roughly the shape of a normal distribution, find what pe…

In the length of of hospitalization study conducted by several cooperating hospitals,a random sample of 64 peptic ulcer patients was drawn from the list of all peptic ulcer ever admitted to the participating hospital and the length of…

22. For a chi-square distribution,find x2\alpha such that a) P(X2 > x2\alpha) = 0:99 when df = 4; b) P(X2 > x2\alpha) = 0:025 when df = 19; c) P(37.652 < X2 < x2\alpha) = 0:045 when df = 25. 23. Find a) t0.…

1. An urn contains 4 balls numbered 1, 2, 3, 4, respectively. Let Y be the number that occurs if one ball is drawn at random from the urn. What is the probability function for Y ? 2. Consider the urn in Exercise 1. Two balls are …

We wish to estimate the mean serum indirect bilirubin level of 4 days old infants.the mean for the sample of 16 infants was found to be 5.98mg/100cc.assume the bilirubin levels in 4 days old infant are approximately normally distribut…

A sample of 60 Grade 11 students' ages was obtained to estimate the mean of all Grade 11 students. The sample mean is 16.4 years and the population standard deviation is 4. What is the point estimate for µ?

Suppose the force acting on a column that helps to support a building is normally distributed with mean 16.0 kips and standard deviation 1.35 kips. What is the probability that the force a. Is at most 17 kips? b. Is betwee…

The automatic opening device of a military cargo parachute has been designed to open when the parachute is 202 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 202 m and standard de…

Suppose a population has a mean of 180 with a standard deviation of 30 pounds. Find the standard deviation of the sampling distribution of the sample means for sample size of 450

A new stockbroker (XYZ) claims that his brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean and std-dev of all ABC broker clients are $18 an…

There are two octahedral dice with faces marked 1 through 8. They are constructed such that the side 8 is 1.5 times as probable as the 2 through 7 and the sum of the probabilities of the 1 and the 8 equals that of the pairs on opposin…

Suppose a population has a mean of 165 with a standard deviation of 20 pounds. Find the standard deviation of the sampling distribution of the sample means for sample size of 60

A manufacturer claimed that at least 95% of the equipment which he supplied to a factory conformed to specification. State the null and alternative hypothesis for each of the following statements

Using the number 1,2,3,4,5 and 6 as the element of the population a. find the mean of the sample of size 3 without replacement b.construct the sampling distribution of the sample mean I. The mean II.The variance III…

A box contains 8 balls. One is numbered 2, two are numbered 3, one is numbered 4, and four are numbered 5. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If th…

Two samples consisting of 21 and 9 observations have variances given by s 1 2 =16 and s 2 2 =8 respectively. Test the hypothesis that the first population variance is greater than the second at a (a) 0.05, (b) 0.01 level of significance.

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Question ID: mtid-4-stid-47-sqid-4351-qpid-70