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 order to compare the mileage yields of 3 kinds of gasoline, several tests were run and the following results were obtained:

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.

(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?

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.

Let X is the advertisement expenditures (in Lakh Rs.) and Y is the sales (in Lakh Rs.). Let the data are

If the coefficient of determination is 0.833, the number of observations and independent variables are 12 and 3, respectively, then Adjusted R² will be 0.84.