Statistics and Probability Answers

Let "X_1, X_2,\u2026.., X_n" be independently and identically distributed b(1, p) random variables. Obtain confidence interval for p using Chebychev’s inequality.

A population consists of four numbesr (3, 8, 10, 15). Consider all possible sample of size 2 that can be drawn without replacement from the population.

Find the following:

a. Population Mean

b. Population Variance

c. Population Standard Deviation

d. The Mean of the sampling distribution of means

e. The Standard deviation of the sampling distribution of means

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:

3.4 2.5 4.8 2.9 3.6

2.8 3.3 5.6 3.7 2.8

4.4 4.0 5.2 3.0 4.8

Assuming that the measurements represent a random sample from a normal population, find a 95% prediction interval for the drying time for the next trial of the paint.

A random sample of 25 tablets of buffered aspirin contains, on average, 325.05 mg of aspirin per tablet, with a standard deviation of 0.5 mg. Find the 95% tolerance limits that will contain 90% of the tablet contents for this brand of buffered aspirin. Assume that the aspirin content is normally distributed.

A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3,900 kilometers. Assume the distribution of measurements to be approximately normal.

a) Construct a 99% confidence interval for the average number of kilometers an automobile is driven annually in Virginia.

b) What can we assert with 99% confidence about the possible size of our error if we estimate the average number of kilometers driven by car owners in Virginia to be 23,500 kilometers per year?

A population consists of four numbesr (3, 8, 10, 15). Consider all possible sample of size 2 that can be drawn without replacement from the population.

Find the following:

a. Population Mean

b. Population Variance

c. Population Standard Deviation

d. The Mean of the sampling distribution of means

e. The Standard deviation of the sampling distribution of means

1.                 A certain restaurant advertises that it puts 0.25 pound of beef in its burgers. A customer who frequents the restaurant thinks the burgers actually contain less than 0.25 pound of beef. With permission from the owner, the customer selected a random sample of 60 burgers and found the mean and standard deviation to be 0.22 and 0.77, respectively.

a.   Test the customer’s assertion at 0.01 level of significance using the critical value approach.

b.   Will you reject Ho in (a) at 0.01 level of significance?

Solution:

a.   Ho: ____________________                  Ha: _____________________

b.   𝛼 = _____________________ ;   critical value: ________________   ; type of test: ___________       c. Criterion region: _____________________________________________________________   d. Test Statistic: ___________________________

Illustrate the qualities of a good measure of central tendency  (4 marks)

Mzee Kobe Bank wished to establish the times in seconds that each ATM transaction takes. A sample of ATM users were observed and the time in seconds each spent at the ATM was as follows:

Time  (seconds)

10-19

20-29

30-39

40-49

50-59

Number of customer

15

60

67

98

2

i. Calculate the coefficent of variation of the waiting time?  ( 6 marks)

The average undergraduate cost for tuition, fees, room, and board for all institutions last year was $26,025. A random sample of 40 institutions of higher learning this year indicated that the mean tuition, fees, room, and board for the sample was $27,690, and the population standard deviation is $5492. At the 0.05 level of significance, is there sufficient evidence that the cost has increased? Use P-Value Method. Find the 95% confidence level of the true mean. Does the confidence interval interpretation agree with the results of the hypothesis test?