A newspaper publisher, trying to pinpoint his market’s characteristics wondered whether newspaper readership in the community is related to readers’ educational achievement. A survey questioned adults in the area on their level of education and their frequency of readership. The results are shown in the following table:
| Frequency of Readership | Level of Educational Achievement | |||
| Professional or postgraduates | College graduates | High school grad | Did not complete high school | |
| Never | 10 | 17 | 11 | 21 |
| Sometimes | 12 | 23 | 8 | 5 |
| Morning or evening | 35 | 38 | 16 | 7 |
| Both editions | 28 | 19 | 6 | 13 |
Do these data provide the sufficient evidence that frequency of newspaper readership in the community differ according to the reader’s level of education?
(i) Calculate expected frequencies for this problem
(ii) State null and alternative hypotheses.
(iii)Calculate the value if the test statistic.
See Answer →(b) A coal-fired power plant is considering two different systems for pollution abatement. The first system has reduced the emission of pollutants to acceptable levels 68 percent of the time, as determined from 200 air samples. The second, more expensive system has reduced the emission of pollutants to acceptable levels 76 percent of the time, as determine from 250 air samples. If the expensive system is significantly more effective than the inexpensive system in reducing pollutants to acceptable levels, then the management of the power plant will install the expensive system. To decide that
(i) State null and alternative hypotheses
(ii) Name the test which is suitable in this situation and why?
(iii)Calculate the value of test statistic and critical value.
(iv)Which system will be installed if management uses a significance level 0.01 in making decision?
See Answer →In a trial, the null hypothesis is that an individual is innocent of a certain crime. Would the legal system prefer to commit a type-1 or type-II error with this hypothesis?
See Answer →In a trial, the null hypothesis is that an individual is innocent of a certain crime. Would the legal system prefer to commit a type-1 or type-II error with this hypothesis?
See Answer →The department of transportation has mandated that the average speed of cars no interstate highways be no more than 70 km per hours in order. To check that the people follow it or not, a researcher took a random sample of 186 cars and found that the average speed was 68 km per hours with a standard deviation 0.6 km per hours.
(a) Find the standard error of the mean
(b) Construct the interval around the sample mean that would contain the population mean 95% of the time.
(c) If the researcher wants to test that the true mean speed on its highways is 70 km per hours or less with 95% confidence then
(i) State null and alternative hypotheses
(ii) Name the test which is suitable in this situation and why?
(iii)Calculate the value of test statistic and critical value.
(iv)Draw the conclusion on the basis of the applied test.
See Answer →i) What is the probability that the mean length of service times is more than and equal to 12 minutes.
ii) Find the 99% confidence interval for the standard deviation of the mean length of service times.
The lifespan (in ‘000 hours) of four LED bulbs of 07 watts are as follows: 40,46,48, 50
(i) Write all samples of size 2without replacement from the above observations.Compute the sampling distribution and find mean and standard error of the distribution.
(ii) Write all samples of size 3 without replacement from the above observations. Compute the sampling distribution and find mean and standard error of the distribution.
(iii) Compare means and standard errors and draw the conclusion.
See Answer →The Z calculated value for testing the following hypothesis is 1.56.
H0 := 100 and H1 :
100
Then the p-value will be 0.256.
See Answer →For testing the pulse rate of one month old child is to be 120 per minute, a researcher measures (per minute) the pulse rate of 10 one month old children and applies sign test and Wilcoxon signed-rank test, then power of the Wilcoxon signed-rank test is more than the sign test.
See Answer →If a researcher wants to half the standard error of the estimator of the mean then he/she will increase the sample size 4 times.
See Answer →If X1, X2, X3, X4 and X5 is a random sample of size 5 taken from anExponential distribution, then estimator T1 is more efficient than T2.
See Answer →
If the probability density function of a random variable X follows F-distribution is
then degrees of freedom of the distribution will be (2,2).
The menstrual cycle in woman following normal distribution has a mean of 28 days and S.D. of 2 days. How frequently would you expect a menstrual cycle of
i) More than 30 days ii) Less than 22 days
See Answer →A hospital specialises in heart surgery. During the year 2018-19, 2000 patients were admitted for treatment. Average payment made by a patient was Rs. 120000 with a standard deviation of Rs 25000. Assuming the distribution of payments to normal, find:
i) The number of patients who paid between Rs. 1,00,000 and Rs. 1,75,000.
ii) The probability that a patient’s bill exceeds Rs. 75,000
iii) The maximum amount paid by the lowest paying one-third patient.
See Answer →In a certain game, Ravi beats Pawan with probability 2/5. They play a series of games until one of them wins six games. Assume that each game is independent of the other. Find the probability that the series will end after 10 games
See Answer →A drunk has five keys on his key chain, and only one will open the front door of his house. He tries each key until he finds the right one. Assume that he is so drunk that he may repeat the wrong key any number of times. On average how many trials he will make to open the front lock of his house.
See Answer →An insurance company models the number of days elapsing between the beginning of a calendar year and the moment a high-risk driver gets into an accident by means of an exponential random variable with parameter . If they expect that 10% of the high-risk drivers will get into an accident during the first 30 days of the calendar year, find the probability that a high-risk driver will get into an accident during the first 40 days of a calendar year.
In a certain book, there is one misprint per two pages, on the average. What is the probability that there are two or more misprints on a randomly chosen page?
See Answer →A coin is biased so that heads appears with probability 2/3 and tails with probability 1/3. This coin is tossed three times. If X denotes the number of heads occurring and Y denotes the number of tails that occur up to the first head, if any, that appears, then determine
i) the joint probability mass function of X and Y.
ii) marginal probability mass functions of the random variables
iii)
A hand of three cards is chosen from a standard deck of 52 cards. You get Rs 3 for each heart in your hand. If X denotes the random variable measuring your gain, then find expected value of X.
See Answer →