A simple random sample of 33 men from a normally distributed population results in a standard deviation of 8.2 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts​ (a) through​ (d) below.

a. Identify the null and alternative hypotheses.

b. Compute the test statistic; χ2 = ___ ​(Round to three decimal places as​ needed.)

c. Find the​ P-value; ​P-value = ____ ​(Round to four decimal places as​ needed.)

d. State the conclusion. (choose one from each ( x, y) set)

In her book Red Ink Behaviors, Jean Hollands reports on the assessment of leading Silicon Valley companies regarding a manager's lost time due to inappropriate behavior of employees. Consider the following independent random variables. The first variable x1 measures manager's hours per week lost due to hot tempers, flaming e-mails, and general unproductive tensions. x1: 1 3 6 2 2 4 10 The variable x2 measures manager's hours per week lost due to disputes regarding technical workers' superior attitudes that their colleagues are "dumb and dispensable". x2: 8 3 2 7 9 4 10 3 (i) Use a calculator with sample mean and sample standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Does the information indicate that the population mean time lost due to hot tempers is different (either way) from population mean time lost due to disputes arising from technical workers' superior attitudes? Use α = 0.05. Assume that the two lost-time population distributions are mound-shaped and symmetric. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 = μ2; H1: μ1 ≠ μ2 H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 ≠ μ2; H1: μ1 = μ2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Do not use rounded values. Round your final answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.

A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.5 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.5 4.3 4.5 5.1 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2 H0: μ1 < μ2; H1: μ1 = μ2 H0: μ1 = μ2; H1: μ1 > μ2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England. Fail to reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England. Reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England. Fail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.

Please outline each step used along the way to solve the problem using excel only with cell numbers and formulas used. Thank you.

Whenever an Alliance Air customer flies on a prepurchased seat, Alliance Air obtains $100 in profits. However, if Alliance Air has more customers seeking a seat then they have prepurchased, Alliance Air is forced to book that passenger on a seat purchased that day. In such a situation, Alliance Air has a profit of -$170 due to the high cost of same-day flights. If not all of their prepurchased seats are taken, then Alliance Air makes a profit of -$20 by selling the seats at a discount to passengers outside of their customer base. Based on their data, Alliance Air knows that number of customers seeking a flight on any day follows a Poisson distribution with mean 40.

Using this information, complete the following tasks/questions:

1. Develop an Excel spreadsheet model which can calculate the daily profits for Alliance Air, given any particular demand for that day and assuming Alliance Air pre-purchased 37 seats on the plane.
2. Using the given demand distribution, set-up your spreadsheet as a simulation model using daily profits as the output. Run the simulation assuming Alliance Air prepurchases 37 seats on the plane. What is the average daily profit in this scenario?
3. How many seats would you recommend Alliance Air to prepurchase if they wanted to maximize their average daily profit? To answer this, modify the number of Pre-Purchased Daily Seats from 30 to 55 (in the increments of 5) and fill in the table provided with statistics about the expected daily profits (Note that the average might keep changing slightly as you record those values, that’s okay). What are the minimum and maximum daily profits if they were to purchase this quantity? What percentage of the time is Alliance Air’s daily profit above 2,250?

In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence, or no effect at all. A sample of 30 participants who have taken the medication has a mean of 105. It is assumed that the data are drawn from a normally distributed population. Did the medication affect intelligence, using α = 0.05?

(a) State hypotheses appropriate to the research question.

(b) Describe what test would you use and state the reasons for your choice.

(c) Draw a conclusion in the context of the problem using the p-value.

(d) Construct a 95% CI for µ. Conclude in the context of the problem.

(e) Compute the power if the true population mean is 110.

home / study / math / statistics and probability / statistics and probability questions and answers / suppose that we fit model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi ... Your question has been answered Let us know if you got a helpful answer. Rate this answer Question: Suppose that we fit Model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi = β0 + ... Suppose that we fit Model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi = β0 + β1x1i + β2x2i + εi , i = 1, …., n, (1) where ε’s are identically and independently distributed as a normal random variable with mean zero and variance σ2, i = 1, …, n , and all the x’s are fixed. a) Suppose that Model (1) is the true model. Show that at any observation yi , the point estimator of the mean response and its residual are two statistically independent normal random variables. b) Suppose the true model is Model (1), but we fit the data to the following Model (2) (that is, ignore the variable x2). yi = β 0 + β 1x1i + εi , i = 1, …., n. Assume that average of x1 =0, average of x2=0. The sum of x1i and x2i equals 0. Derive the least-squares estimator of β1 obtained from fitting Model (2). Is this least-squares estimator biased for β1 under Model (1)?

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 while that client’s process was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be 0.21. 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 that the mean for the process should be 12. The hypothesis test suggested by Quality Associates is as follows: ± H H :1 2 :1 2 0 a m m 5 Corrective action will be taken any time H0 is rejected. The samples listed in the following table were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data are available in the file Quality. Sample 1 Sample 2 Sample 3 Sample 4 11.55 11.62 11.91 12.02 11.62 11.69 11.36 12.02 11.52 11.59 11.75 12.05 11.75 11.82 11.95 12.18 11.90 11.97 12.14 12.11 11.64 11.71 11.72 12.07 11.64 11.71 11.72 12.07 11.80 11.87 11.61 12.05 12.03 12.10 11.85 11.64 11.94 12.01 12.16 12.39 11.92 11.99 11.91 11.65 12.13 12.20 12.12 12.11 12.09 12.16 11.61 11.90 11.93 12.00 12.21 12.22 12.21 12.28 11.56 11.88 12.32 12.39 11.95 12.03 11.93 12.00 12.01 12.35 11.85 11.92 12.06 12.09 11.76 11.83 11.76 11.77 12.16 12.23 11.82 12.20 11.77 11.84 12.12 11.79 12.00 12.07 11.60 12.30 12.04 12.11 11.95 12.27 11.98 12.05 11.96 12.29 12.30 12.37 12.22 12.47 12.18 12.25 11.75 12.03 11.97 12.04 11.96 12.17 12.17 12.24 11.95 11.94 11.85 11.92 11.89 11.97 12.30 12.37 11.88 12.23 12.15 12.22 11.93 12.25 1. Conduct a hypothesis test for each sample at the 0.01 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 conjecture of 0.21 for the population standard deviation appear reasonable? 3. Compute limits for the sample mean x around 12 m 5 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If x exceeds the upper limit or if x 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? Can you show it in excel of how you get the answers, Thanks

What is the purpose of using correlation as well as the interpretation of the correlation coefficient? In your video response, please describe at least 2 examples of an extremely low relationship among variables and an extremely high relationship among variables. Finally, discuss the two most common statistical techniques for determining relationships of variables.

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a​ two-candidate election, if a specific candidate receives at least 55​% of the vote in the​ sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters. Complete parts​ (a) through​ (c) below.

a. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1​%? The probability is nothing that a candidate will be forecast as the winner when the population percentage of her vote is 50.1​%. ​(Round to four decimal places as​ needed.)

b.

c.

d.

In a random sample of 13 residents of the state of Washington, the mean waste recycled per person per day was 1.6 pounds with a standard deviation of 0.43 pounds. Determine the 98% confidence interval for the mean waste recycled per person per day for the population of Washington.

Statistical significance tests do not tell the researcher what we want to know nor do they evaluate whether or not our results are important. They tell us only whether or not the results of a study were due to chance. Therefore, how do researchers go about doing this? In your video response, please discuss the relationship of the p-value in relation to the level of significance. Lastly, please provide an example of a Type I and Type II errors.  

Pinworm: In Sludge County, a sample of 40 randomly selected citizens were tested for pinworm. Of these, 8 tested positive. The CDC reports that the U.S. average pinworm infection rate is 12%. Test the claim that Sludge County has a pinworm infection rate that is greater than the national average. Use a 0.10 significance level.

(a) What is the sample proportion of Sludge County residents with pinworm? Round your answer to 3 decimal places. p̂ =

(b) What is the test statistic? Round your answer to 2 decimal places. zp hat =

(c) What is the P-value of the test statistic? Round your answer to 4 decimal places. P-value =

(d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0

(e) Choose the appropriate concluding statement.

The data supports the claim that the infestation rate in Sludge County is greater than the national average.

There is not enough data to support the claim that that the infestation rate in Sludge County is greater than the national average.

We reject the claim that the infestation rate in Sludge County is greater than the national average.

We have proven that the infestation rate in Sludge County is greater than the national average.

A teacher gives the following assignment to 200 students: Check the local newspaper every morning for a week and count how many times the word “gun” is mentioned on the “local news” pages. At the end of the week, the students report their totals. The mean result is 85, with a standard deviation of 8. The distribution of scores is normal. a. How many students would be expected to count fewer than 70 cases? b. How many students would be expected to count between 80 and 90 cases? c. Karen is a notoriously lazy student. She reports a total of 110 cases at the end of the week. The professor tells her that he is convinced she has not done the assignment, but has simply made up the number. Are his suspicions justified?

The multiple regressions serve to explain the behavior of one variable (dependent variable) though a set of some explanatory variables for which we can find a logical/theoretically founded relationship with the dependent variable.

Please discuss three business situations (either real or a business situation) with proposed set of 5 explanatory variable. Could you define the expected sign (positive or negative) of these selected explanatory variables?

As e have discussed the usage of the dummy variables propose at least in one of the three cases you discuss previously one or two dummy variables you think are good explanatory variables for the case you are discussing.