In the current tax year, suppose that 3% of the millions of individual tax returns have errors or are fraudulent. Although these errors are often well concealed, let’s suppose that a through IRS audit (done by you of course) will uncover them. If a random 100 tax returns are audited what is the probability that the IRS will uncover at most 4 fraudulent returns? Create an Excel spreadsheet that may give you an idea about this probability. Hint: Use the RAND() function for every tax return. The RAND() function generates a random number between 0 and 1. If the RAND() function gives you a number that is less than or equal to 0.03 then you can assume that the return contains error. Otherwise you can assume that the return does not contain any error. You can press F9 on your keyboard to regenerate a new instance. You may have to create enough instances to come up with a good approximation of the probability value. You can also find the exact probability using Binomial Distribution. What does it mean if an IRS auditor uncovers no more than 3 fraudulent/erroneous returns for every 100 tax returns?

Please in Excel.

According to a study done by Pew Research Center, 210 out of 500 adult Americans believe that marriage is now obsolete.

a. Find the mean and standard deviation of the sampling distribution of ?̂; the sample proportion of adult Americans who believe marriage is obsolete.

b. In a random sample of 500 adult Americans, what is the probability that less than 35% believe marriage is obsolete?

c. What is the probability that in a random sample of 500 adult Americans between 40% and 50% believe marriage is obsolete?

d. Would it be unusual if a random sample of 500 adult Americans resulted in 250 or more who believe marriage is obsolete? (remember that unusual is more than 2 standard deviations from the mean)? Why or why not?

A machine that is programmed to package 3.30 pounds of cereal is being tested for its accuracy. In a sample of 49 cereal boxes, the sample mean filling weight is calculated as 3.39 pounds. The population standard deviation is known to be 0.14 pound. [You may find it useful to reference the z table.]

a-1. Identify the relevant parameter of interest for these quantitative data.

-The parameter of interest is the proportion filling weight of all cereal packages.

-The parameter of interest is the average filling weight of all cereal packages.

a-2. Compute its point estimate as well as the margin of error with 99% confidence. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

b-1. Calculate the 99% confidence interval. (Use rounded margin of error. Round your final answers to 2 decimal places.)

b-2. Can we conclude that the packaging machine is operating improperly?

Yes, since the confidence interval contains the target filling weight of 3.30.

No, since the confidence interval does not contain the target filling weight of 3.30.

No, since the confidence interval contains the target filling weight of 3.30.

Yes, since the confidence interval does not contain the target filling weight of 3.30.

c. How large a sample must we take if we want the margin of error to be at most 0.03 pound with 99% confidence? (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and round up your final answer to the next whole number.)

Consider a population with a known standard deviation of 13.6. In order to compute an interval estimate for the population mean, a sample of 40 observations is drawn. [You may find it useful to reference the z table.]

a. Is the condition that X− is normally distributed satisfied? Yes No

b. Compute the margin of error at a 99% confidence level. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

c. Compute the margin of error at a 99% confidence level based on a larger sample of 240 observations. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

d. Which of the two margins of error will lead to a wider confidence interval?

99% confidence with n = 40.

99% confidence with n = 240.

In order to construct a confidence interval for the population variance, a random sample of n observations is drawn from a normal population. Use this information to find χ²_α/2,df and χ²_{1- α/2,df} under the following scenarios. (Round your answers to 3 decimal places. You may find it useful to reference the appropriate table: chi-square table or F table)

rev: 06_10_2019_QC_CS-170121

1. Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−2.13 ≤ z ≤ −0.35) =

2. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 14.6; σ = 3.9

P(10 ≤ x ≤ 26) =

3. A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 82 and standard deviation σ = 30. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)

(a) x is more than 60


(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 125 (borderline diabetes starts at 125)

Find the missing value required to create a probability distribution, then find the standard deviation for the given probability distribution. Round to the nearest hundredth.

x / P(x)
////////
0 / 0.2
1 / 
2 / 0.13
3 / 0.03
4 / 0.05

The manager of the Burrard Credit Union wishes to know if there is a significant difference
between male and female customers’ interest in a proposed new type of savings certificate. A
survey of 200 randomly selected customers has yielded the following data:

INTEREST

SEX Strong Moderate Weak Total
Male 30 25 25 80
Female 60 40 20 120
Total 90 65 45 200

(a) What percentage of customers shows a strong or moderate interest in these savings
certificates? [2 marks]

ANSWER

(b) What percentage of customers is male AND shows a strong or moderate interest in
these savings certificates? [2 marks]

ANSWER

(c) What percentage of male customers do NOT show a strong interest in these savings
certificates? [2 marks]

ANSWER

(d) Among those customers who show a weak interest in these types of savings certificates,
what is the probability that they are a female?

. A chain that specializes in healthy and organic food would like to compare the sales performance of two of its primary stores in the state of Massachusetts. These stores are both in urban, residential areas with similar demographics. Assuming equal variances, a comparison of the weekly sales randomly sampled over a period of nearly two years for these two stores yields the following information (reported in $1,000). Is there a difference in sales between the two stores?

1. State the null and alternative hypotheses
2. What is the test statistic?
3. Using a .05 significance level, what is the decision rule?
4. Show the test statistic and essential calculations.
5. What do you conclude? State you findings in a sentence

Let X1. . . . Xn be i.i.d f(x; θ) = θ(1 − θ)^x x = 0.. Is there a function of θ for which there exists an unbiased estimator of θ whose variance achieves the CRLB? If so, find it

A developmental psychologist prepares a video tape which demonstrates the “conservation of matter”. She selects 8 young children from a day care and first tests them on this type of problem (that matter is the same volume regardless of shape) and records the number of correct responses. She then shows the video tape and re-measures their ability to solve these problems. Below are the results:
# correct           # correct
Child       before tape           after tape
1       3               8
2       0               6
3       6               4
4       2               8
5       9               10
6       8               6
7       6               2
8       5               10

State the independent and dependent variables.
State the Null Hypothesis in words and symbols
Compute the appropriate statistic
What is the decision?
State the Full conclusion in words.

Question 1: We believe that the proportion of households in California who own a dog is less than the proportion of households in Texas who own a dog. In two independent polls, it was found that 210 out of 500 Californa households own a dog and 302 out of 500 Texas households own a dog. Use a 0.05 significance level.

Question 2: For my one property, I have 104 units out of them I have received 5 non-renewal letters, with those 2 had massive fights and complaints through-out their stay at the property. I have my other property which has 238 units out of them I have received 7 non-renewal letters, with those 4 had massive fights and complaints through-out their stay at the property. find the 95% confidence interval.

Lindsay is 27 years old and has a new job in web development. She wants to make sure that she is financially sound by the age of 55, so she plans to invest the same amount into a retirement account at the end of every year for the next 28 years.

Briefly define the measures R, Q, and s. What are the advantages of using the standard deviation over range and interquartile range?