A simple random sample of 50 accounts is taken from an account receivables portfolio of XYZ Ltd and the average account balance is $650. The population standard deviation o is known to be $70. Test the hypothesis that the population mean account balance is greater than a. $620 using the p-value approach and a 0.05 level of significance. b. Test the hypothesis that the population mean account balance is less than $800 using the critical value approach and a 0.05 level of significance. Test the hypothesis that the population mean account balance is different from $750. using the p-value approach and a 0.05 level of significance. C.

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is known that 76% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 66 new products, find the following probabilities. (Round your answers to four decimal places.) (a) within 2 years 47 or more fail (b) within 2 years 58 or fewer fail (c) within 2 years 15 or more succeed (d) within 2 years fewer than 10 succeed

statistics. HELP!

Take a simple experiment of rolling a pair of balanced dice. Each die has six sides, each side contains one to six spots. Let us define the random variable x to be the sum of the spots on the two dice. Display the probability mass function and the distribution function for the random variable x.

Exercise 14-4 Algo Consider the following competing hypotheses: H0: ρxy ≥ 0 HA: ρxy < 0 The sample consists of 34 observations and the sample correlation coefficient is –0.58. Use Table 2. a. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic b. Approximate the p-value. p-value < 0.005 0.005 < p-value < 0.01 0.01 < p-value < 0.025 0.025 < p-value < 0.05 c. At the 5% significance level, what is the conclusion to the test? H0, we conclude that the population correlation coefficient between x and y is significantly different from zero. rev: 11_14_2015_QC_CS-31836 References

An experiment to compare the spreading rates of five different brands of yellow interior latex paint available in a particular area used 4 gallons (J = 4) of each paint. The sample average spreading rates (ft²/gal) for the five brands were x_1. = 462.0, x_2. = 512.8, x_3. = 437.5, x_4. = 469.3, and x_5. = 532.1. The computed value of F was found to be significant at level α = 0.05. With MSE = 480.8, use Tukey's procedure to investigate significant differences between brands. (Round your answer to two decimal places.)
w =

Which means differ significantly from one another? (Select all that apply.).

x_1. and x₂

x_1. and x₃

x_1. and x_4.

x_1. and x_5.

x_2. and x_3.

x_2. and x_4.

x_2. and x_5.

x_3. and x_4.

x_3. and x_5.

x_4. and x_5.

There are no significant differences.

1.     Introduction: Brief description of the study including the purpose and importance of the research question being asked.

2.     What is the null hypothesis? What is the research hypothesis?

3.     Participants/Sampling Method: Describe your sampling method. What is your sample size? Who is your population of interest? How representative is the sample of the population under study?

4.     Data Analysis: Describe the statistical analysis. What is your variable? What is its level of measurement? What is your alpha level?

5.     Results & Discussion: Did you reject the null hypothesis? What information did you use to lead you to your conclusion? Was your p value greater than or less than your alpha? NOTE: You can just make up numbers, but include your made-up p value

Demand data on "Service Orders" for a particular service enterprise for the previous 12 months is as follows: 550, 652, 673, 707, 725, 752, 780, 797, 815, 836, 850, and 872. Problem 3b) Use the following three methods and prepare three forecasting tables with errors for the given demand data. • a 3-month Weighted Moving Average with the weights 0.6, 0.3, and 0.1 with the maximum weight going for the most recent data point into the past • Exponential Smoothing with smoothing constant = 0.9 • Linear Trend Regression

Suppose a geyser has a mean time between eruptions of 66 minutes. If the interval of time between the eruptions is normally distributed with standard deviation

24 minutes​, answer the following question.

What is the probability that a random sample of 38 time intervals between eruptions has a mean longer than 76 ​minutes?

The probability that the mean of a random sample of 38 time intervals is more than 76 minutes is approximately __________

​(Round to four decimal places as​ needed.)

A Gallup Poll released in December 2010 asked 1019 adults living in the Continental U.S. about their belief in the origin of humans. These results, along with results from a more comprehensive poll from 2001 (that we will assume to be exactly accurate), are summarized in the table below:

Calculate the actual number of respondents in 2010 that fall in each response category as well as the expected number, assuming that the population follows the 2001 distribution. (please round to the nearest whole number)

Conduct a chi-square test and state your conclusion.

The value of the test statistic is: .... (please round to two decimal places)

The p-value for this test is: .... (please round to four decimal places; you can use CHISQ.DIST Excel function)

State the conclusion.

The mayor of a large city claims that 25 % of the families in the city earn more than $ 100,000 per year; 55 % earn between $ 30,000 and $ 100,000 (inclusive); 20 % earn less than $ 30,000 per year.

In order to test the mayor’s claim, 285 families from the city are surveyed and it is found that:

90 of the families earn more than $ 100,000 per year;
135 of the families earn between $ 30,000 and $ 100,000 per year (inclusive);
60 of the families earn less $ 30,000.

Test the mayor’s claim based on 2.5 % significance level.

* Make sure you turn in your code (take a screen shot of your code in R)and answers. Conduct the hypothesis
and solve questions by using R.
2) A random sample of 12 graduates of a secretarial school averaged 73.2 words per minute
with a standard deviation of 7.9 words per minute on a typing test. What can we conclude,
at the .05 level, regarding the claim that secretaries at this school average less than 75
words per minute on the typing test? (You may treat the number of words that a secretary
types in one minute as being normally distributed.)

The number of buses that arrive at a bus stop during a one-hour time span can be modeled as a Poisson process with rate λ (see Remark below). Now suppose a passenger has just arrived at the bus stop and starts waiting. Let Y be the time (in unit of hours) she needs to wait to see the first bus.

(a) Is Y a discrete or continuous random variable? Find the set of all possible values of Y .

(b) For a possible value y of Y , find P(Y > y).

(c) Find the distribution (pdf/pmf) of Y and identify it as one of the “named” distributions with corresponding parameter(s).

In the same setting as in the previous question, suppose we know there is exactly one bus arrival on a time interval [0, 1] (the unit is hour). Let Y be this single arrival time.

(d) Find the set of possible values of Y .

(e) For a possible value y of Y , find P(Y ≤ y).

(f) Find the pdf/pmf of Y and identify it as one of the “named” distributions with corresponding parameter(s).

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found to be 110​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct an 80​% confidence interval about mu if the sample​ size, n, is 28. ​(b) Construct an 80​% confidence interval about mu if the sample​ size, n, is 13. ​(c) Construct a 70​% confidence interval about mu if the sample​ size, n, is 28. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

A person wants to invest $10,000 into stocks: a high tech company (T) with an expected annual return of 12% and a risk index of 8; and a regulated power company (P) with an expected annual return of 6% and a risk index of 2. To limit risk, the combined portfolio risk must be no more than 6 and the proportion of investment in T must be less than 60%. Find the portfolio that will maximize the annual return R while meeting the risk limitations.

a. Formulate the Investment Portfolio problem with the requirement of investing up to $10,000, and solve it graphically.

b. Compute the increase in annual return if the total investment is increased by $1,000.

c. Compute the increase in annual return if the constraint of portfolio risk index is increased from 6 to 7.

Here is a list of scores on the Traditionalism Index for the ANES unique group of

respondents who simultaneously rated Christian Fundamentalists and Atheists

at 100 on the Feeling Thermometer:

7, 10, 5, 6, 5, 8, 5, 12, 4, 11, 11, 9, 10, 13, 8, 8, 7

Use these raw data to the find the mean, median, mode, variance, and standard

deviation.