Physicians at a clinic gave what they thought were drugs to 860860 patients. Although the doctors later learned that the drugs were really placebos, 5656 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.530.53. Test the hypotheses that the proportion of patients improving is >0.53

1. The larger the calculated χ² value in a goodness-of-fit test, the _______ likely the data fits the hypothesized distribution.

2.

If the observed frequencies are exactly equal to the expected frequencies in a chi-square test, the value of χ² is:

a. close to 1

b. a large positive value

c. 0

d. a very small positive value

3. A chi-square statistic can be used to analyze contingency tables:

True or False

4. The chi-square statistic for a 6x4 contingency table will have ____ degrees of freedom.

5. The chi-square test can be used to determine if there is a significant difference between two sample proportions:

True or False

6. Which of the following null hypotheses cannot be tested with a chi-squared test?

a. H_o: the two variables defining the contingency table are independent.

b. H_o: the population distribution is a normal distribution.

c. H_o: the true category proportions are the same for all of the population.

d. H_o: the true population means are the same for all of the populations

7. To test the null hypothesis that a population proportion is p = 0.40 using a sample size of n = 12, we use the ____________ distribution.

a. t

b. normal

c. binomial

d. chi-square

8. The null hypothesis that two processes produce the same proportion of defectives can be written:

a. p = 0

b. x₁/n₁ = x₂/n₂

c. p₁ - p₂ = 0

d. x/n = 0

9. The chi-square distribution is symmetrical:

True or False

10. The test statistics for a small-sample test concerning proportion is the ___________. [hint: use all lowercase letters]

Tukey's Post test. Alpha = .05. Group I: 0, 2, 2, 0, 1 Group II: 4, 6, 1, 5, 4 Group III: 1, 3, 0, 1, 0. Step by Step how to solve

QUESTION: Suppose you work in the quality assurance department of a chemical processing plant and it is your responsibility to ascertain whether the viscosity of a certain chemical remains within a prescribed limit. To that end you measure fluid samples using a viscometer.

a. The viscosities of a sample of 10 fluids processed during the day shift were measured to have the following results (Pa.s): 71, 45, 54, 75, 50, 49, 63, 55, 48, 50. Determine the range within which the true mean of the fluid samples from the day shift will be with a 95% confidence.

b. You then proceed to the measure the viscosities of a sample of 10 fluids processed during the night shift. You obtain the following measurements (Pa.s): 73, 45, 59, 75, 53, 58, 72, 54, 42, 52. Determine the range within which the true mean of the fluid samples from the night shift will be with a 95% confidence.

c. Can you state with a 95% probability that the viscosity of the fluid being produced during the day shift is different than the night shift? Frame your response in the form of a hypothesis test.

The mean score on a science assessment for 59 male high school students was 319.5 and the standard deviation 2.5. The mean test score on the same test for 40 female high school students was 298.9 and the standard deviation was 1.2. For this assessment, the population standard deviation for males is σ = 2.3 and the population standard deviation for females is σ = 2.0. At a =. 02 , can you support the claim that mean scores on the science assessment for male high school students were higher than for the female high school students?

Answer: a. Claim:


Ho:

Ha:

b. LTT, RTT or TTT ?


c. Hypothesis testing to use:


Why?





d. Standardized test statistic (formula and value)



e. P-value



f. Decision:




g. Interpretation: At  

A survey across generations of workers gathered data on engagement at work. The results for a sample of​ 1,000 workers are in the accompanying contingency table. At the 0.10 level of​ significance, is there evidence of a significant relationship between generation and level of engagement in the​ workplace?

Millennials Gen Xers Baby Boomers Traditionalists Engaged 100 116 90 18 Not Engaged 190 149 134 17 Actively Disengaged 56 65 59 6 What are the null and Alt. Hypothesis?

Please answer! This assignment is due in an hour.

When choosing an item from a group, researchers have shown that an important factor influencing choice is the item's location. This occurs in varied situations such as shelf positions when shopping, filling out a questionnaire, and even when choosing a preferred candidate during a presidential debate. In this experiment, five identical pairs of white socks were displayed by attaching them vertically to a blue background that was then mounted on an easel for viewing. One hundred participants from the University of Chester were used as subjects and asked to choose their preferred pair of socks. In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in the center. In this experiment, 34 subjects chose the pair of socks in the center. Are these data evidence of the "center stage effect"? Follow the four-step process (Hint: if subjects are choosing a pair of socks at random from the five positions, what would be the probability of selecting the pair in the middle? This is the value of p in the null hypothesis).

Premier Consulting’s two consultants, Avery and Baker, can be scheduled to work for clients up to a maximum of 160 hours each over the next four weeks. A third consultant, Campbell, has some administrative assignments already planned and is available for clients up to a maximum of 140 hours over the next four weeks. The company has four clients with projects in process. The estimated hourly requirements for each of the clients over the four-week period are as follows:

Client Hours

A 180 B 75 C 100 D 85

Hourly rates vary for the consultant–client combination and are based on several factors, including project type and the consultant’s experience. The rates (dollars per hour) for each consultant–client combination are as follows:

Client

Consultant A B C D

Avery 100 125 115 100

Baker 120 135 115 120

Campbell 155 150 140 130

a. Develop a network representation of the problem.

b. Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing?

c. New information shows that Avery doesn’t have the experience to be scheduled for client B. If this consulting assignment is not permitted, what impact does it have on total billings? What is the revised schedule? I NEED EXCEL FILE THAT HAS SPREAD SHEET AND SENSITIVITY REPORT to solve this problem

Why is Tukey's method more powerful than Bonferroni's method?

Constructa 99% confidence interval for the population mean, µ, AND State what type of Interval you use (ZInterval, TInterval, 1-PropZInterval). A sample of 22 professors had a mean amount of experience of 10.8 years with a standard deviation of 3.3 years. Assume the population is normally distributed

A company maintains two offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of Dollars) is as follows:

Office	1	1	2	2
Employee	1	2	3	4
Salary	55.6	43.2	65.2	43.2

a) Suppose two of these employees are randomly selected from among the four (without replacement). Determine the sampling distribution of the sample mean salary X.

b) Suppose one of the two offices is randomly selected. Let X1 and X2 denote the salaries of the two employees. Determine the sampling distribution of X.

c) How does E(X) from parts (a) and (b) compare to the population mean salary?

Government standards limit the airborne amount of a known cancer causing gas. A company using such a substance in its production process limits the exposure of its employees to the gas by shutting down production when the amount of the gas reaches 3 ppm(parts per million) with a standard deviation of 0.5 ppm.

(2) If you were the plant manager and you are told management wants as little down time as possible, would you choose a larger or a smaller value of alpha to test whether the amount of gas is dangerous? Explain.

(2) If you were an employee in the plant, would you want the choice of alpha to be larger or smaller?     Explain.

(5) A random sample of 50 air specimens from various sensors in the plant yielded an average of 3.1 ppm. Will this sample data indicate the company should shut down production given their criteria described above? Use alpha = 0.01.

(2) Describe both Type I and Type II errors in the context of this problem.

(5) Calculate the probability of Type II error if in fact the true average plant level is 3.1 ppm. Use alpha = 0.01.

(1) What is the value of the Power of the test in this case?

(5) Calculate the probability of Type II error if in fact the true mean plant level is 3.1 ppm when alpha = 0.05.

(1) What is the Power of the test now?

(2) What do the findings of parts e, f , h , and i confirm about the relationships between alpha, beta and the Power of the test?

Podcessories manufacturers a several accessories for a popular digital music player. The company is trying to decide whether to discontinue one of the items in this product line. Discontinuing the item would save the company $600,000 in fixed costs (comprised of leases on building and machinery) during the coming year. However, the company is anticipating that it might receive an order for 60,000 units from a large discount retailer that could prove to be very profitable. Unfortunately, the company is being forced to make a decision about renewing the leases required to continue this item before it will know if it will receive the large order from the discount retailer. The variable cost per a unit for this item is $6.00. The regular selling price of the item is $12.00 per unit. However, the company has offered the discount retailer a price of $10.50 per unit due to size of its potential order. Podccessories believes there is a 60% chance it will receive the order from the discount retailer. Additionally, it believes general demand for this product (apart from the discount retailer's order) will vary between 45.,000 to 115,000 units with a most likely outcome of 75,000 units. Build a spreadsheet model which can be used for simulation to forecast the total profit of the company.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a marketing survey, a random sample of 998 supermarket shoppers revealed that 280 always stock up on an item when they find that item at a real bargain price.(a) Let p represent the proportion of all supermarket shoppers who always stock up on an item when they find a real bargain. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)

lower limit
upper limit

Give a brief explanation of the meaning of the interval.

5% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.    5% of all confidence intervals would include the true proportion of shoppers who stock up on bargains.95% of all confidence intervals would include the true proportion of shoppers who stock up on bargains.

(c) As a news writer, how would you report the survey results on the percentage of supermarket shoppers who stock up on items when they find the item is a real bargain?

Report the margin of error.Report p̂ along with the margin of error.    Report the confidence interval.Report p̂.

What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)

16.

–/5

Questions 28-35 are related to the following The following table is the regression summary output for a model depicting the impact of years of schooling (EDUCTION) on hourly wage rate (WAGE). SUMMARY OUTPUT Regression Statistics Multiple R 0.47100 R Square Adjusted R Square 0.22106 Standard Error Observations 1000 ANOVA df SS MS F Significance F Regression 1 284.5202001 2.3433E-56 Residual 142.4243578 Total 999 182662.1158 Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 1.6551 -3.8378 0.0001 -9.6000 -3.1041 EDUCATION 0.0000 Use the following calculations first: ∑xy = 310428.68 x = EDUCATION n = 1000 y = WAGE x̅ = 13.907 y̅ = 20.83103 ∑x² = 204011 28 The model predicts that wage rises by _______ for each additional year of schooling. a $2.16 b $2.11 c $2.05 d $1.95 29 The predicted WAGE for 16 years of schooling is, a $26.44 26.44 b $25.67 25.67 c $24.92 24.92 d $23.93 23.93 30 SSE = ______ a 142139.51 b 140718.11 c 139310.93 d 137917.82 31 The measure of closeness of fit, or measure of dispersion of observed expenditure on food around the regression line is, a 10.24 b 11.93 c 12.12 d 12.85 32 The fraction of the variations in WAGE explained by years of schooling is, a 0.2218 b 0.2440 c 0.2562 d 0.2690 33 se(b₁) = ______ a 0.312 b 0.225 c 0.198 d 0.116 34 The test statistic to test the hypothesis that years of schooling has no impact on wage is, a 18.227 b 16.868 c 14.645 d 9.936 35 The upper end of the 95% interval estimate for the population slope parameter is, a 3.16 b 2.95 c 2.18 d 1.88