Statistics and Probability Answers

a) Distinguish between regression analysis and correlation analysis

Records show that the average farm size in a particular region has increased over the last 70 years. This trend might be explained, in part, by the inability of small farms to compete with the prices and costs of large-scale operations and to produce a level of income necessary to support the farmers’ desired standard of living. An agribusiness researcher believes the average size of farms has continued to increase since 2007 from a mean of 471 hectares. To test this, a random sample of 23 farms was selected from official government sources and their sizes recorded. The sample yielded a mean farm size of 498.78 hectares and a standard deviation of 46.94 hectares. Test the hypothesis, using either the p-value approach or the classical approach at the 0.05 level of significance.

Consider the example where the average net income for all sole proprietor CPA’s was found to be $74,914 in a survey done five years ago. A new survey is conducted by taking a random sample of 112 currently, practising sole proprietor CPAs to determine if this average net income figure has changed. The sample average net income is calculated to be $78,695, and it is known that the population standard deviation of net incomes for sole proprietor CPA’s is $14,530. Use the sample data to establish if there is sufficient evidence to conclude that the average net income for sole proprietor CPA’s has changed in the last 5 years.

b) Sales personnel for Boomerang Distributors are required to submit weekly reports listing the customer contacts made during the week. A sample of 61 weekly contact reports showed a mean of 22.4 customer contacts per week for the sales personnel. The sample standard deviation was 5 contacts.
i. Use the large-sample case to develop a 95% confidence interval for the mean number of weekly customer contacts for the population of sales personnel.
i. Assume that the population of weekly contact data has a normal distribution. Use the
t distribution with 60 degrees of freedom to develop a 95% confidence interval for the mean number of weekly customer contacts.
ii. Compare your answers for parts (1) and (ii). Comment on why in the large-sample case it is permissible to develop interval estimates using the procedure in part (i) even though the t distribution may also be applicable

a) The sample standard deviation of P/E ratios for stocks listed on the Sydney Stock Ex-change is s = 7.8. Assume that we are now interested in estimating the population mean P/E ratio for all stocks listed on the Sydney Stock Exchange in July 2004. How many stocks should be included in the sample if we want a margin of error of 2? Use a 95% confidence level.

do you know the answer to:

Suppose personal daily water usage in Darwin City is normally distributed, with a mean of 18 litres and a standard deviation of 6 litres.
a) What percentage of the population uses between 10 and 20 litres?
b) What is the probability that a person uses less than 10 litres?
c) If the local government wants to give a tax rebate to the 20% of the population that use the least amount of water. What should the government use as the maximum water limit for a person to qualify for a tax rebate?
d) Suppose the governments’ proposed tax rebate causes a shift in the average water use from 18 litres to 14 litres per person per day, but causes no shift in the standard deviation. What limit should be set on water use if 20% of the population is to receive a tax rebate?

Hoemwork#2:Provide the best answer for each of the questions below making sure you round at each step of an equation. Your final answer may be rounded to the second place.
NOTE ON EXPRESSING POSITIVE AND NEGATIVE VALUES: When your answer is positive, THERE IS NO NEED TO INDICATE IT by using a + sign. The lack of a negative sign implies a number is positive, including a + sign will result in your answer being wrong. If your number is negative, designate it as negative by putting a negative sign in front of the number, like this: -1.34 or -.34. DO NOT put your negative sign in parentheses, like this: (-).34 or your answer will be marked wrong.
NOTE ON EXPRESSING ANSWERS IN DECIMAL WITHOUT WHOLE NUMBERS: If your answer to any problem, for example when you are computing proportions, lacks whole numbers, such as .34, DO NOT put a zero infront of the decimal or you will be marked wrong.

1. The Walker Hunters are accepting new recruits. The following is a distribution ages of people interested in becoming recruits.

The percentage of American men who say they would marry the same woman if they had to do it over again is 65% what is the probability that in a group of 10 married American men, no more than 3 will claim that they would marry the same woman again? what is a probability that at least 6 will say this?

Probability of india winning match against Pakistan is 0.5 find the probability that india's 2nd win occur s in 3rd test in a 5 match series?

Calculate the standard deviation of the mark 2,3,6,2,5,0,2.