A particular area in a town suffers a high burglary rate. A sample of 100 streets...

A particular area in a town suffers a high burglary rate. A sample of 100 streets is taken,
and in each of the sampled streets, a sample of six similar houses is taken. The table below
shows the number of sampled houses, which have had burglaries during the last six months.

No. of houses burgled x	0	1	2	3	4	5	6
No. of streets f	39	38	18	4	0	1	0

(i) (a) State any assumptions needed to justify the use of a binomial model for the number of
houses per street which have been burgled during the last six months.
(b) Derive the maximum likelihood estimator of X bar, the probability that a house of the
type sampled has been burgled during the last six months.
(c) Determine the probabilities for the binomial model using your estimate of X bar, and,
without doing a formal test, comment on the fit.

(ii) An insurance company works on the basis that the probability of a house being burgled
over a six-month period is 0.18. Carry out a test to investigate whether the binomial
model with this value of p provides a good fit for the data.

NOTE:THERE WAS A MISTAKE ON (b) IT IS ESTIMATOR OF X BAR NOT ESTIMATOR OF P but i have corrected it

Expert Solution

orchestra answered 1 year ago

A random sample of 200 high school students in a particular town showed that 122 smoke...

A random sample of 200 high school students in a particular town showed that 122 smoke on a regular basis. Find the 99% confidence interval estimating the population percentage for smokers at this high school.

In a small town, there are 5 high school districts. Each district includes 100 high school...

In a small town, there are 5 high school districts. Each district includes 100 high school students. In total, there are 500 high school students in the town including 240 male students and 260 female students. Researchers would like to select a sample of 200 students. (a) Explain how the sample can be obtained using random cluster sampling. (b) Explain how the sample can be obtained using stratified random sampling. (c) Explain how the sample can be obtained using systematic...

Suppose 90% of a sample of 100 randomly selected homes in Town A and 80% of...

Suppose 90% of a sample of 100 randomly selected homes in Town A and 80% of a sample of 50 randomly selected homes in Town B rely on the public water supply for drinking water. Compute the test statistic for a hypothesis test to compare the population proportion of homes that rely on the public water supply for drinking water in Town A to the proportion in Town B. Assume that the conditions for a hypothesis test for the difference...

A sample of 9 residents’ incomes in a particular town yields the following descriptive statistics: $19,000...

A sample of 9 residents’ incomes in a particular town yields the following descriptive statistics: $19,000 $20,000 $27,000 $38,000 $112,000 $45,000 $22,000 $49,000 $32,000 What is the interquartile range for this sample?

For a sample of 100 honors students at a particular college, a sociologist collected the following...

For a sample of 100 honors students at a particular college, a sociologist collected the following information on the year of school and the willingness to help the school raise donations by making telephone calls to alumni: Willingness To Help Year in College Freshman Sophomore Junior Senior Willing 15 16 15 15 Unwilling 15 14 5 5 Using these data, test the null hypothesis that willingness to help raise donations does not differ by year in school. Use a .05...

High Rate - 2.410% Investment Rate - 2.458% Price per $100 - 99.390806 This is a...

High Rate - 2.410% Investment Rate - 2.458% Price per $100 - 99.390806 This is a 91-day T-bill with par value $100 issued on January 10, 2019 and maturing on April 11, 2019. (a) Calculate the rate of interest that a purchaser of this bill would earn over the period, and convert this to an annual investment rate. Verify that your answer corresponds to the published investment rate. (b) Calculate the discount rate and verify that your answer corresponds to...

Consider the following data for a particular sample period when returns were high: &n

Consider the following data for a particular sample period when returns were high: Portfolio P Market Portfolio Average Return 32% 28% Beta 1.3 1.0 Standard Deviation 40% 30% Calculate Jensen’s Alpha, the Sharpe ratio and Treynor’s ratio for both portfolio P and the Market. The T-bill rate during this period was 5%. By which measures did portfolio P outperform the market?

A random sample of 100 students at a high school was asked whether they would ask...

A random sample of 100 students at a high school was asked whether they would ask their father or mother for help with a homework assignment in science. A second sample of 100 different students was asked the same question in history. If 46 students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for help, test the claim whether the difference between the proportions is due...

4. (24) The average starting salary of a random sample of 100 high school students was...

4. (24) The average starting salary of a random sample of 100 high school students was found to be $31,840. The population standard deviation for all such individuals is known to be $9,840. a. (12) Ten years ago, the average starting salary was $25,000. Does the sample data support the claim that the starting salary for this group has increased? Use alpha = 0.05. b. (6) Describe in general Type I and Type II errors and the Power of the...

Q: The average starting salary of a random sample of 100 high school students was found...

Q: The average starting salary of a random sample of 100 high school students was found to be $31,840. The population standard deviation for all such individuals is known to be $9,840. a. (12) Ten years ago, the average starting salary was $25,000. Does the sample data support the claim that the starting salary for this group has increased? Use alpha = 0.05. b. (6) Describe in general Type I and Type II errors and the Power of the test....

Question