A population of values has a normal distribution with μ = 109.2 and σ = 65.6 . You intend to draw a random sample of size n = 90 .

Find the probability that a sample of size n = 90 is randomly selected with a mean greater than 96.1. P( ¯ x > 96.1) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. License

n 1944​, an organization surveyed 1100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?" Of the 1100 adults​ surveyed, 396 indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 374 indicated that they were total abstainers. Complete parts​ (a) and​ (b) below. ​(a) Determine the sample proportion for each sample. The proportions of the adults who took the 1944 survey and the recent survey who were total abstainers are nothing and nothing​, respectively. ​(Round to three decimal places as needed Has the proportion of adults who totally abstain from alcohol changed. Use the a=0.10 level of significance Determine the null and alternative hypothesis Find the test statistics for this hypothesis test Interpret the P value State conclusion for hypothesis test

Is the difference between the mean annual salaries of statisticians in Region 1 and Region 2 more than $8000? To​ decide, you select a random sample of statisticians from each region. The results of each survey are shown to the right. At α=0.10, what should you​ conclude? Answer A-E

Region 1

x1 = $68,300

standard deviation = $8,750

n1 = 47

Region 2

x2 = $63,000

standard deviation = $9,275

n2 = 40

A. What are the alternative and null hypotheses? Express them mathematically.

B. Determine the critical values and rejection regions

C. Calculate the standardized test statistic

D. Choose the correct answer below

a) Fail to reject H null, at the​ 1% significance​ level, there is sufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

b) Reject H null, at the​ 1% significance​ level, there is sufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

c) Reject H null, at the​ 1% significance​ level, there is insufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

d) Fail to reject H null, at the​ 1% significance​ level, there is insufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

A study reports that 36% of companies in a Country A have three or more female board directors. Suppose you select a random sample of 100 respondents.

What is the probability that the sample will have between 29% and 38% of companies in Country A that have three or more female board directors?

1. In the Excel data file, the tab labeled Question 1 contains data on the number of times boys and girls raise their hands in class. Conduct the t-test: Two-Sample Assuming Equal Variances.
2. Males 9,8,4,9,3,8,10,8,9,10,7,6,12
3. Females 3,5,1,2,6,4,3,6,7,9,7,3,7,6,8,8

a. What is the null hypothesis?

b. What is the research hypothesis?

c. Why run a Two-Sample Assuming Equal Variances t-test?

d. Interpret the findings. What are the results of the hypothesis test? Can you reject the null hypothesis?

Insomnia and Education. A random-digit telephone dialing procedure was employed to collect data on 575 study participants. The researcher classified each participant into one of four education categories (college graduate, some college, high school graduate, and high school dropout) as well as two categories of insomnia status (normal sleeper or chronic insomnia). One dependent variable of interest to the researchers was a quantity measure of daytime functioning called the Fatigue Severity Scale (FSS). The data were analyzed using an ANOVA model a Write the model underlying the analysis bThe researcher reported that “the Insomnia×Education interaction was not statistically significant”. Interpret this result in context. Illustrate with a graph. (4 Marks c The researchers discovered that the mean FSS was significantly greater for normal sleepers than for people with chronic insomnia. Interpret this result in context. d The researcher reported that the main effect of Education was statistically significant. Interpret this result in context.

Use EXCEL and formulas

Linear program problem whose output follows determines how many necklaces, bracelets, rings, and earrings a jewelry store should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions.

MAX 100X1+120X2+150X3+125X4

S.T.

1) X1+2X2+2X3+2X4<108

2) 3X1+5X2+X4<120

3) X1+X3<25

4) X2+X3+X4>50

Use the microsoft excel solver method to find the solution and the sensitivity report.

Which resource should the company increase and why?

Use the Financial database from “Excel Databases.xls” on Blackboard. Use Total Revenues, Total Assets, Return on Equity, Earnings Per Share, Average Yield, and Dividends Per Share to predict the average P/E ratio for a company. Use Excel to perform a forward selection regression analysis. Assume a 5% level of significance. Based on your final model, what is the p-value from the test of the overall model? Write your answer as a number and round to 3 decimal places.

Excel Data: https://drive.google.com/file/d/1TQG5r2wzLGk--75whZXyb0SDTHZTWS0S/view?usp=sharing

A television station wishes to study the relationship between viewership of its 11 p.m. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 p.m. news is found for each sample. The results are given in the table below.

(a) Let p₁, p₂, p₃, and p₄ be the proportions of all viewers in each age group who watch the station’s 11 p.m. news. If these proportions are equal, then whether a viewer watches the station’s 11 p.m. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H₀ that p₁, p₂, p₃, and p₄ are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05. (Round your answer to 3 decimal places.)

χ2

=            

so

H₀: independence

(b) Compute a 95 percent confidence interval for the difference between p₁ and p₄. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

95% CI: [ , ]

You are interested in understanding whether mentally ill offenders are better able to avoid re-arrest if they are assigned a mental health case manager upon their release from jail or prison. You study a sample of formerly incarcerated people with mental health diagnoses. You are comparing people with a case manager to those who do not have one (measured as: has a case manager / does not have a case manager), on whether or not they are re-arrested within one year (measured as two categories: rearrested vs. not re-arrested). 1. Write a one-tailed, directional research hypothesis that is appropriate for the above research project. 2. Specify your dependent and independent variables, and at what level they are measured. 3. Write the corresponding null hypothesis for this research study. 4. Specify the type of statistical test you would use in this situation and why. 5. Assume that you find that 50% of people with a case manager are re-arrested, and 60% of people without a case manager are re-arrested within one year. If your statistical analysis produced a test value of 2.70 (and you have 1 df), what would this tell you (assuming you use alpha=.05 as the cut-off for your rejection region)? 6. Write up your results as if you were reporting them in an official report. Examples of appropriate write-ups are available in the videos and powerpoints for each kind of statistical test.

A sports reporter for a local newspaper is working on a story about small college basketball players. A reporter for a major sports magazine found that large college basketball players score 25 points per game. The local paper reporter believes that small college players score more points per game than large college players. She watches several small college basketball games and follows 25 players. Those 25 players score an average of 27.3 points per game with a standard deviation of 1.25 points. At a significance level of .05, can the reporter conclude that small college basketball players score more points per game than large college players?

A researcher tests whether job security and life satisfaction are related. In this study, he observes the following frequencies. If he computes a test for independence at a .05 level of significance, then what is the decision for this test?

21. What were the total number of participants?

22. What is the null hypothesis?

23. What is the research hypothesis?

24. What is the chi-square value?

25. What is your conclusion regarding the null hypothesis?

A group of biochemistry researchers developed a new medication for treating depression. To assess if the new medication is effective at treating depression, the researchers obtained a sample of depressive patients from a local clinic. The patients were then randomly assigned into taking the medication for a month or not. In addition, the patients were also randomly assigned into receiving psychotherapy for a month or not. At the end of the study, the patients were asked to fill out a depression inventory in which a higher score indicates more depression. The data are below. What can be concluded with α = 0.01?

                Psychotherapy

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Medication: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Psychotherapy: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Interaction: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Medication: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Psychotherapy: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a medication difference in depression.There is no medication difference in depression.    

There is a psychotherapy difference in depression.There is no psychotherapy difference in depression.    

There is a medication by psychotherapy interaction in depression.There is no medication by psychotherapy interaction in depression.