Compare ‘all data’ of Maradi and Zinder using a histogram. Do both regions have the same distribution? If they are different, how are they different? Explain your answer using modality and skewness.Can you answer using R.

GW Maradi

GW ZInder

Please Answer both parts of the question below

Answer the flowing questions that summarize the chapter.

Part A-

How do confidence intervals and significance tests relate?

Part B-

What are the conditions (or assumptions) that must be checked when performing a significance test for the slope of a regression line?

The state of California has a mean annual rainfall of 23 inches, whereas the state of New York has a mean annual rainfall of 53 inches ( Current Results website, October 27,2012). Assume that the standard deviation for both states is 2 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken.

a. Show the probability distribution of the sample mean annual rainfall for California.

b. What is the probability that the sample mean is 1 inch of the population mean for California?

c. What is the probability that the sample mean is within 1 inch of the population mean for New York?

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 43.9 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.As the confidence level increases, the margin of error remains the same.     As the confidence level increases, the margin of error increases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.As the confidence level increases, the confidence interval increases in length.     As the confidence level increases, the confidence interval remains the same length.

How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)

Need it in Excel format in detail.

Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken during a time in which that client’s process was operating satisfactorily. The sample standard deviation for these data was .21; hence, with so much data, the population standard deviation was assumed to be .21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated the mean for the process should be 12. The hypothesis test suggested by Quality Associates follows.

Corrective action will be taken any time  is rejected.

The following samples were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data are available in the data set Quality.

Managerial Report

1. Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any, should be taken. Provide the test statistic and p-value for each test.

2. Compute the standard deviation for each of the four samples. Does the assumption of .21 for the population standard deviation appear reasonable?

3. Compute limits for the sample mean  around  such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If  exceeds the upper limit or if  is below the lower limit, corrective action will be taken. These limits are referred to as upper and lower control limits for quality control purposes.

4. Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased?

An economist wants to estimate the variance of employee test scores. A random sample of 38 scores had a sample standard deviation of 10.4. Find a 95% confidence interval for the population variance.

Data collected over a long period of time showed that 1 in 1000 high school students like mathematics. A random sample of 30,000 high school students was surveyed. Let X be the number of students in the sample who like mathematics

a) What is the probability distribution of X?

b) What distribution can be used to approximate the distribution of X? Explain.

c) Find the approximate probability of observing a value of X equal to 40 or more?

d) Find the approximate probability of observing a value of X between 35 and 40 inclusive ?

Suppose that the probability that a passenger will miss a flight is 0.09420. Airlines do not like flights with empty​ seats, but it is also not desirable to have overbooked flights because passengers must be​ "bumped" from the flight. Suppose that an airplane has a seating capacity of 58 passengers.

​(a) If 60 tickets are​ sold, what is the probability that 59 or 60 passengers show up for the flight resulting in an overbooked​ flight?

​(b) Suppose that 64 tickets are sold. What is the probability that a passenger will have to be​ "bumped"?

​(c) For a plane with a seating capacity of 53 ​passengers, how many tickets may be sold to keep the probability of a passenger being​ "bumped" below 5%?

Jobs for the homeless! A philanthropic foundation bought a used school bus that stops at homeless shelters early every weekday morning. The bus picks up people looking for temporary, unskilled day jobs. The bus delivers these people to a work center and later picks them up after work. The bus can hold 139 people, and it fills up every morning. Not everyone finds work, so at 11 A.M. the bus goes to a soup kitchen where those not finding work that day volunteer their time. Let us view each person on the bus looking for work as a binomial trial. Success means he or she got a day job. The random variable r represents the number who got jobs. The foundation requested a P-Chart for the success ratios. For the past 3 weeks, we have the following data.

Make a P-Chart. (Use 4 decimal places.)

List any out-of-control signals by type (I, II, or III). (Select all that apply.)

Out-of-control signal I occurs on day 11.Out-of-control signal I occurs on day 14.Out-of-control signal III occurs on days 4 and 5.Out-of-control signal III occurs on days 14 and 15.There are no out-of-control signals.

Interpret the results.

1. Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Life expectancy is a statistical measure of average time a person is expected to live, based on a number of demographic factors. Mathematically, life expectancy is the mean number of years of life remaining at a given age, assuming age-specific mortality rates remain at their most recently measured levels. Last year the average life expectancy of all the Life Insurance policyholders in Ontario at age 65 was 22.3 years (meaning that a person reaching 65 last year was expected to live, on average, until 87.3). The insurance company wants to determine if their clients now have a longer average life expectancy, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample data is provided in the excel file. Answer the following questions. Results should be support by excel output.

a. Construct a 95% and 99% confidence intervals for the true average life expectancy. Use t-distribution and Descriptive Statistics function from Data Analysis. Interpret each Confidence interval and comment on the difference between the 95% and 99% interval.

b. Write the null and alternative hypotheses for this test:

c. In this context, describe a Type I error possible. How might such an error impact Life Insurance company’s decision regarding the premium structure?

d. What is the value of the t-test statistic?

e. What is the associated P-value?

f. State the conclusion using α = 0.05. Do it using both P-value and critical value.

A balanced die with six sides is rolled 60 times. For the binomial distubtion of X = Numbers of 6’s, what is n, what is p, and what is q Find the mean and standard deviation of the distribution of X. What do these values tell you? If you observe X = 2, would you be skeptical that the die is balanced? Explained why, based on the mean and standard deviation of . How long would the value of X Have to be in order to prove evidence that the die is unbalanced? Hint a binomial distribution with a high number of trails approximates the normal distribution.

Provide one example each of both a Type I and Type II error that could occur
when running predictive engines relevant to sports betting. Which is likely to
be more costly and why?

1. Music seems to be everywhere in society, and psychologists have investigated its effects on a variety of performances. For example, suppose an experimenter created three equivalent groups of eight people each and asked each person to perform a proofreading task on a short research paper. Subjects in group A1 performed the task with no music playing in the background, subjects in group A2 performed the task with a selection of oldies playing in the background, and subjects in groups A3 performed the task while listening to hard rock. The dependent variable was the errors detected out of a possible 50. Suppose the following scores were obtained:

1.a.Analyze the scores with a one-factor between-subjects ANOVA to answer the question: Did the music condition affect the number of errors detected by a subject? Use α= .05. If needed, use the Tukey HSD test for multiple (pairwise) comparisons.

1.b.Report the results of this experiment as it would appear in a research paper.

In a survey of 865 registered voters in Washington, 408 people are in favor of making Pi Day an official holiday.

1. Which of the following would be the appropriate format for a confidence interval for the proportion of Washington voters who are in favor of making Pi Day an official holiday?

• A. a<σ<b
• B. a<¯x<b
• C. a<μ<b
• D. a<s<b
• E. a<p<b
• F. a<ˆp<
• G. a<x<b
• H. a<n<b

• 
  2. Using the format you selected above, find the 95% confidence interval for Pi Day support. (Round to four decimal places.)
  a=? b=?

• 
  3. What is the margin of error for this confidence interval? (Round to four decimal places.)
  ε=?

The cholesterol level in children aged 10-15 is assumed to follow a normal distribution with a mean of 175 and a standard deviation of 20.

What is the probability of selecting a child at 10-15 years with cholesterol level higher than 190?

What is the probability of selecting a child at 10-15 years with cholesterol level between 165 and 190?

What is the interval of cholesterol level of a child 10-15 years higher than 75% and lower than top 10% of children?