QUESTION 2

Using the following table. Write a concise, relevant, accurate and precise interpretation of the SPSS output provided assuming the dependent variable is Total Perceived Stress. Include supporting statistical evidence.

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The following question is based on scenario 2: Researchers are interested in seeing how sitting for long periods of time can influence cardiovascular health. They ask people how many hours per day they sit, and then they measure their blood pressure to see if they are associated. They expect that as hours spent sitting increases, blood pressure will also increase.

A. What is the best statistical test to use to analyze the hypothesis in scenario 2?

Structural Equation Model

z-test

Independent sample t-Test

Correlation Coefficient

Dependent sample t-Test

Factor Analysis

z-score

One-way ANOVA

B. Which of the following is the null hypothesis for scenario 2?

Ho: µ₁ = µ₂ = µ₃

H₀: X = µ

rxy = 0

Scenario 3. A 5^th grade school teacher believes that she has an exceptionally gifted group of students in her class this year. She learns that the national average score on the 5^th grade annual test is 150, with a standard deviation of 30. She wants to compare her student’s scores to the national average.

A. What is the null hypothesis for scenario 3?

HO: µ1 = µ2

HO: µ1 = µ2 =µ3

r = 0

H0: X = µ

B. What is the alternative hypothesis for scenario 3?

H1: m1 < m2

r ≠ 0

H1: X1 ≠ X2 ≠ X3

H1: X ≠ µ

C. What is the appropriate test statistic to use for scenario 3?

correlation coefficient

regression

z-test

dependent samples t-test

One-way ANOVA

independent samples t-test

A study was conducted to explore the effects of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 got only water (control). Treatment 2 got 1g of ethanol per kg of body weight, and treatment 3 got 2g ethanol per kg of body weight. The amount of REM sleep in a 24hr period was recorded, in minutes. Data are below: Treatment 1: 63, 54, 69, 50, 72

Treatment 2: 45, 60, 40, 56

Treatment 3: 31, 40, 45, 25, 23, 28

(f) Calculate 90% confidence intervals for all pairwise comparisons of treatment means using the uncorrected method. Create a letter code table to summarize your results, then interpret the results in context.

(g) Now calculate 90% confidence intervals for all pairwise comparisons using the Bonferroni correction. Create a letter code table, and interpret your results in context. Do any of the results differ from part (f)?

The National Longitudinal Study of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next 10 years?” Here is a two-way table of the responses by gender:

1. How many individuals are described in this table?
2. How many females were among the respondents?
   
   
3. The percent of females among the respondents was about %.
   
4. Your percent from the previous exercise is part of
   • the marginal distribution of sex.
   • the marginal distribution of opinion about marriage.
   • the conditional distribution of sex among adolescents with a given opinion.
   
   
5. What percent of females thought that they were almost certain to be married in the next 10 years?
   %
   
6. Your percent from the previous exercise is part of
   • the conditional distribution of sex among those who thought they were almost certain to be married.
   • the marginal distribution of opinion about marriage.
   • the conditional distribution of opinion about marriage among women.

in a random sample of 8 Laptops, the mean repair cost per laptop was $90.46 and the standard deviation was $19.30. Assume the variable is normally distributed and construct a 90% confidence interval forμ. Round your answer two decimal place

Provide two examples of how regression analysis could be used in the business world. (if you are currently employed, think about how your firm could use regression analysis to evaluate and improve business performance).

The number of hours 12 students watched television during the weekend and the scored of each student who took a test the following Monday are listed below.

a) Find linear regression equation using correct notation (for statistics) the given problem, round coefficients to 3 decimals. (no sentence here)

b) What is value of the slope and its meaning in context of the problem? Make sure you include units.

c) What is the value of the correlation coefficient, does this indicates a negative or positive

association and is correlation strong, weak or neither?

d) If a student watched 4 hours of TV during the weekend, what is the student predicated test score

on the Monday exam? (to one decimal)

e) If a student watched 6 hours of TV during the weekend, what is the student predicated test score

on the Monday exam? (to one decimal)

f) What is residual value for a student that watched 6 hours of TV during the weekend?

Explain what it means, in context of the problem

Can people tell the difference between a female nose and a male nose? Eight Caucasian males and eight Caucasian females posed for nose photos. The article states that none of the volunteers wore nose studs or had prominent nasal hair. Each person placed a black Lycra tube over his or her head in such a way that only the nose protruded through a hole in the material. Photos were then taken from three different angles: front view, three-quarter view, and profile. These photos were shown to a sample of undergraduate students. Each student in the sample was shown one of the nose photos and asked whether it was a photo of a male or a female; and the response was classified as either correct or incorrect. The accompanying table was constructed using summary values reported in the article. Is there evidence that the proportion of correct sex identifications differs for the three different nose views? Test the appropriate hypotheses using a .05 significance level. (Use 2 decimal places.)

χ² =
P-value interval

The data  ---Select--- support do not support the hypothesis that the proportions of correct sex identifications differ for the three different nose views.

Match the following:

A market researcher investigated consumer preferences for Coca-Cola and Pepsi before a taste test and after a taste test. The following table summarizes the results from a sample of 200 consumers:

She wanted to perform a chi-square test to see if there is evidence of a difference in preference for Coca-Cola before and after the taste test by allowing a 10% probability of incorrectly concluding that there is a difference when there is in fact no difference.

a) The test will involve _________ degree(s) of freedom.

b) The critical value of the test is _________.

c) The value of the test statistic is _________.

d) Give the above results, should the null hypothesis will be rejected?

One timber company claims that the amount of usable lumber in the trees being harvested in ClearCut is approximately normally distributed, with a mean of 256 cubic feet per tree and a standard deviation of 42 cubic feet.

a) What is the probability that the amount of usable lumber in a randomly selected tree is less than 250 cubic feet?

b) If a decision is made not to harvest the smallest 20% of the trees, they will be harvested when they are bigger. What is the smallest size of tree allowed to be cut?

c) If 49 trees are randomly selected from ClearCut, what is the probability that the average amount of usable lumber in the 49 selected trees is less than 250 cubic feet?

4. Julie visits the local park 90 times, and sees her favorite pigeon 38 times. Let p be the probability that Julie sees the pigeon on any given visit, and assume that whether Julie sees the pigeon on some visit is independent of whether she sees the pigeon on any other visit.

(a) Construct a 90% two-sided confidence interval for p.

(b) Julie believes that there is a 50% chance that she sees the pigeon when she visits the park. Is your interval in part (a) consistent with that belief? Explain your answer.

(c) Test Julie’s claim from part (b) with a hypothesis test. Use a significance level of α = 0.05. Perform the test by comparing a test statistic to a critical value found in the tables in the back of your textbook.

(d) Perform the test in part (c) using a p-value.

In one of Boston’s public parks, mugging in summer months has been a serious issue. A police cadet took a random sample of 10 days and compiled the data. For each day, x represents the number of police officers on duty in the park and y represents the number of reported muggings on that day. A scatter plot has been provided in the following.

1. (a) What information can we learn from the above scatter plot?

2. (b) One wishes to use the linear model for this question. Please specify the theoretical linear model and the common assumptions.

3. (c) Based on the following SAS output, please write out the regression line.

1. (d) Can you predict y value when x = 30? Why or why not?

2. (e) Please construct a 95% confidence interval for the slope.

3. (f) Overall is this model useful? (Please set up hypotheses and report the result from SAS output).

4. (g) Find the sample correlation coefficient.

In one of Boston’s public parks, mugging in summer months has been a serious issue. A police cadet took a random sample of 10 days and compiled the data. For each day, x represents the number of police officers on duty in the park and y represents the number of reported muggings on that day. A scatter plot has been provided in the following.

1. (a) What information can we learn from the above scatter plot?

2. (b) One wishes to use the linear model for this question. Please specify the theoretical linear model and the common assumptions.

3. (c) Based on the following SAS output, please write out the regression line.

1. (d) Can you predict y value when x = 30? Why or why not?

2. (e) Please construct a 95% confidence interval for the slope.

3. (f) Overall is this model useful? (Please set up hypotheses and report the result from SAS output).

4. (g) Find the sample correlation coefficient.