The data in the accompanying table represent the rate of return of a certain company stock for 11​ months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts ​(a) through ​(d) below.

Click the icon to view the data table.​(a) Treating the rate of return of the index as the explanatory​ variable, x, use technology to determine the estimates of

beta 0β0

and

beta 1β1.

The estimate of

beta 0β0

is

nothing.

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

The estimate of

beta 1β1

is

nothing.

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

​(b) Assuming the residuals are normally​ distributed, test whether a linear relation exists between the rate of return of the​ index, x, and the rate of return for the company​ stock, y, at the

alphaαequals=0.10

level of significance. Choose the correct answer below.

State the null and alternative hypotheses.

A.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1greater than>0

B.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1not equals≠0

C.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0not equals≠0

D.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0greater than>0

Determine the​ P-value for this hypothesis test.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.) State the appropriate conclusion at the

alphaαequals=0.10

level of significance. Choose the correct answer below.

A.Reject

Upper H 0H0.

There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.  

B.Reject

Upper H 0H0.

There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

C.Do not reject

Upper H 0H0.

There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.  

D.Do not reject

Upper H 0H0.

There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

​(c) Assuming the residuals are normally​ distributed, construct a​ 90% confidence interval for the slope of the true​ least-squares regression line.

Lower​ bound:

nothing

​(Round to four decimal places as​ needed.) Upper​ bound:

nothing

​(Round to four decimal places as​ needed.) ​(d) What is the mean rate of return for the company stock if the rate of return of the index is

3.153.15​%?

The mean rate of return for the company stock if the rate of return of the index is

3.153.15​%

is

nothing​%.

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

Click to select your answer(s).

Rate of Return

PrintDone

In a random sample of​ males, it was found that 26 write with their left hands and 214 do not. In a random sample of​ females, it was found that 66 write with their left hands and 436 do not. Use a 0.05 significance level to test the claim that the rate of​ left-handedness among males is less than that among females. Complete parts​ (a) through​ (c) below.

Let Y be the sum of two fair six-sided die.

(a) Find the PMF of Y.

(b) What is the expected value of Y ?

(c ) What is the standard deviation of Y ?

(d) Interpret the standard deviation you found in the last part in context of the experiment.

(e) Find the CDF of Y.

(f) Use the CDF of Y to find the probability that the sum of the dice will be strictly between six and ten. Answers calculated using the PDF will receive no credit.

Describe the two ways to test for multicollinearity. Which one do you prefer?

Source: Dingley, C., & Roux, G. (2014). The role of inner strength in quality of life and self-management in women survivors of cancer. Research in Nursing & Health, 37(1), 32-41.

Introduction

Dingley and Roux (2014) studied inner strength, depression symptoms, and selected demographic variables to predict quality of life (QOL) and self-management in women survivors of cancer. This predictive correlational study was conducted with a convenience sample of 107 women with cancer. “The strongest predictors of QOL were depressive symptoms, inner strength, and time since diagnosis. The strongest predictors of self-management were depressive symptoms and inner strength” (Dingley & Roux, 2014, p. 32).

Relevant Study Results

Selected instruments used to measure the study variables in the Dingley and Roux (2014) study are presented in this section with a focus on reliability testing.

“Depression. The Center for Epidemiological Studies Depression Scale (CES-D; Radloff, 1977) was used to assess depressive symptomatology. The CES-D is one of the most widely used self-report instruments for epidemiologic studies of depression and has been used in primary care, psychiatric, and related clinical and forensic settings. The 20-item instrument measures depressive affect, somatic symptoms, positive affect, and interpersonal relations. For each experience related to depression, the respondent selects the value (0, 1, 2, or 3) that best describes how frequently the experience occurred during the previous week. Total scores of 15 to 21 indicate mild to moderate depressive symptoms; scores over 21 indicate the respondent has experienced major depressive symptoms. Cronbach’s alpha in this study was 0.90.

Inner strength. The Inner Strength Questionnaire (ISQ) is a 27-item self-report instrument written at a fourth grade level (by Flesch Kincaid Grade Index). Respondents are asked to indicate their level of agreement with each item statement using a 5-point Likert-type scale (strongly agree, agree, slightly agree, disagree, strongly disagree). The ISQ assesses four factors representing dimensions of the theory (i.e., Anguish and Searching, Connectedness, Engagement, and Movement). Total scores can be calculated, as well as scores for each subscale. The maximum possible total score is 135, with higher scores indicating a higher presence of inner strength. Each sub-scale of the ISQ had a Cronbach’s alpha > 0.80 (Anguish and Searching 0.85, Connectedness 0.95, Engagement 0.85, and Movement 0.83). Internal consistency reliability of the total ISQ was α = 0.91. Cronbach’s alpha for the present study was 0.89.

Quality of life and spiritual well-being. The tool selected to measure QOL was the Functional Assessment of Cancer Therapy—Spiritual WELL-Being (FACTSp), one instrument from the FACIT Measurement System, a collection of QOL questionnaires targeted at the management of chronic illness. The FACIT measurement system is considered appropriate for use with patients with any form of cancer as well as other chronic illness conditions (e.g., HIV/AIDS, multiple sclerosis) and in the general population using a slightly modified version. The FACT-Sp incorporates the domain of spiritual well-being (SpWB) in addition to the four primary domains of physical (PWB), social/family (SWB), emotional (EWB), and functional well-being (FWB). The SpWB scale is 12 questions that measure a sense of meaning and peace and the role of faith in illness… The SpWB had a Cronbach’s alpha of 0.93 in the study sample. Cronbach’s alphas for the subscales were PWB = 0.85, SWB = 0.80, EWB = 0.79, FWB = 0.88, and SpWB = 0.83” (Dingley & Roux, 2014, pp. 35-36).

Based on the information provided from the Dingley and Roux (2014) study, which scale has the lowest reliability or Cronbach’s alpha coefficient? What random error did this scale have for this study? Was this a study strength or weakness?

What is hypothesis testing? Explain fully and provide a real-world example.

To demonstrate flavor aversion learning (that is, learning to dislike a flavor that is associated with becoming sick), researchers gave one group of laboratory rats an injection of lithium chloride immediately following consumption of saccharin-flavored water. Lithium chloride makes rats feel sick. A second control group was not made sick after drinking the flavored water. The next day, both groups were allowed to drink saccharin-flavored water. The amounts consumed (in milliliters) for both groups during this test are given below.

(a) Test whether or not consumption of saccharin-flavored water differed between groups using a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)


State the decision to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.    

(b) Compute effect size using eta-squared (η²). (Round your answer to two decimal places.)
η² =

In a study of treatments for very painful​ "cluster" headaches,

159159

patients were treated with oxygen and

154154

other patients were given a placebo consisting of ordinary air. Among the

159159

patients in the oxygen treatment​ group,

111111

were free from headaches 15 minutes after treatment. Among the

154154

patients given the​ placebo,

3434

were free from headaches 15 minutes after treatment. Use a

0.050.05

significance level to test the claim that the oxygen treatment is effective. Complete parts​ (a) through​(c) below.

In a survey of 3,778 adults concerning complaints about​ restaurants, 1,436 complained about dirty or​ ill-equipped bathrooms and 1,213 complained about loud or distracting diners at other tables. Complete parts ​(a) through​ (c) below.

a. Construct a 90​% confidence interval estimate of the population proportion of adults who complained about dirty or​ ill-equipped bathrooms.

b. Construct a 90% confidence interval estimate of the population proportion of adults who complaied about loud or distracting diners at other tables.

(round to 4 decimal placed)

Exercise 13-60 (LO13-2, LO13-3, LO13-5)

Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below.

a. Write out the regression equation

2. How much damage would you estimate for a fire 4 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)

3. Determine and interpret the coefficient of determination. (Round your answer to 3 decimal places.)

   c-2. Fill in the blank below. (Round your answer to one decimal place.)

4. Determine the correlation coefficient. (Round your answer to 3 decimal places.)

5. State the decision rule for 0.01 significance level: H₀ : ρ = 0; H₁ : ρ ≠ 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

6. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

5. A professor theorizes that science students perform differently on multiple choice tests than on essay tests. The professor recruited 6 science students and had them take both types of test. Their test scores were recorded. The data are given in the following table. Based on the data, can you support the professor’s theory? Perform an appropriate test at α = 0.01.

• Which hypothesis test should be used?

 one-sample Z-test  one-sample t-test  independent-samples t-test  paired-samples t-test

• Step 1. State the hypotheses (both in words and in symbols)

• H₀:

• H₁:

• Step 2: α = 0.01

• Step 3: Use SAS to calculate a test statistic (write a SAS code for reading in the data set and analyzing it, and upload your SAS code on the Cyber campus website). Copy and paste the relevant SAS output. Report the obtained test statistic and calculate effect size (Cohen’s d).

• Step 4: Make a decision.

• Step 5: State a conclusion (You should include the test statistic, p-value, effect size, and a verbal interpretation of the result).

A researcher is interested in the effects of a psychedelic drug in treating post-traumatic stress disorder (PTSD). To assess if the psychedelic may be effective in attenuating the severity of PTSD symptoms, she performs a pilot experiment to compare the effects of the psychedelic to the commonly‑prescribed selective serotonin reuptake inhibitor (SSRI) Sertraline in individuals diagnosed with PTSD. The amount of the psychedelic was selected based on an online forum in which recreational drug users describe their drug-taking experiences. Previous research has indicated that 100 mg Sertraline is an effective amount for the general population in clinical settings. Individuals with PTSD were randomly assigned to one of two treatment conditions: Psychedelic or Sertraline. The dependent variable is a score on the PTSD Checklist (PCL); a lower score corresponds to fewer PTSD symptoms. The scores are presented in the table below.

1. State the H₀for the experiment above. Please use appropriate notation
2. Perform the Unpaired t-test on excel. Treat the Sertraline group scores as “Variable 1” and the Psychedelic group scores as “Variable 2”. Report the results of the statistical analysis below. Be sure to include the df, the obtained statistic, and the p-value in your answer. Please round all answers to two decimal places.

1. t(_____) = _____, p = _____.
2. What do you conclude based on these results?

3. For Excel: subtract each Sertraline score from the Psychedelic score and compute the mean of these differences. Calculate standard deviation of differences using Excel function: =stdev.s. Calculate the margin of error in the confidence interval using the Excel function: =confidence.t(alpha, standard deviation, number of difference scores). Add and subtract the margin of error to and from the mean of the differences to obtain the upper and lower limits, respectively. Report the 95% confidence interval for the difference between means here: (____, ____). Are your conclusions about the 95% confidence interval consistent with the results you reported in question 2b above, and, if so, why?
4. Report the 95% confidence interval for the psychedelic group here: (____, ____).

              Report the 95% confidence interval for the sertraline group here: (____, ____).

Excel: use the =confidence.t(alpha, SD of the group, sample size) function to determine the confidence interval for each group: this will give you the margin of error. Also, compute the means of each group. Next, add and subtract the margin of error to the mean of each group to get the set of confidence limits. Inspect the confidence intervals and determine if there is a statistically significant difference between the two groups. Are these results consistent with the results you reported in question 3 above?

5. Compute the “Difference between means” in Excel by subtracting the mean of the psychedelic group from the mean of the sertraline group and p-value from the statistical test. Fill the spaces below to define the meaning of the obtained p-value and include the “Difference between means” value in your answer.

There is a ___________ probability of obtaining a mean difference at least as large as ________________ units under the condition that the null hypothesis is true.

6. According to the quick plot of the data, determine if there enough evidence/reason to claim heterogenous variances. Name the test that could be performed in the case of unequal variances. _______________________

7. Now imagine that this was a one-group, pretest-posttest design. The severity of the volunteers’ PTSD symptoms was measured using the PCL before psychedelic administration (pretest) and then afterwards (posttest). Those scores are presented below.

   Subject	Pretest	Posttest
   1	25	15
   2	24	18
   3	25	13
   4	27	13
   5	28	12
   6	30	11
   7	26	7
   8	27	23
   9	27	25
   10	28	18
   11	25	22

8. Perform paired t-test on excel. Try to achieve positive values in your results by selecting “Report differences as: by treating Pretest as “Variable 1” and Posttest as “Variable 2”. Report the results of the statistical analysis below. Be sure to include the df, the obtained statistic, and the p-value in your answer. Please round all answers to two decimal places.
9. t(_____) = _____, p = _____.
10. What do you conclude based on these results?
11. For Excel/other software users; subtract each posttest score from the pretest score and compute the mean of these differences. Use the standard deviation and confidence interval formulas above to complete this problem. Report the 95% confidence interval for the mean of differences here: (____, ____). Note: the center of this interval should be the mean of the difference. Are your conclusions about the 95% confidence interval consistent with the results you reported in question 8d above, and, if so, why?
12. Someone in the research team advises the researcher to compare the 95% confidence interval for the pretest scores to the 95% confidence interval for the posttest scores. Why is this analysis incorrect for these data? Hint: think about what is analyzed in a paired t-test.

Exercise 13-58 (LO13-2, LO13-3)

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

1. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Round your answer to 4 decimal places.)

2. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.050 significance level. (Round intermediate calculations and final answer to 3 decimal places.)

3. Develop the regression equation for effective heating based on wattage.

A new school district superintendent preparing to reallocate resources for physically impaired students wanted to know if the schools in the district differed in the distribution of physically impaired. The superintendent tested samples of 20 students from each of the five schools and found 5 physically impaired (and 15 unimpaired) students at School 1, 5 physically impaired (and 15 unimpaired) at School 2, 6 (and 14) at School 3, 4 (and 16) at School 4, and 7 (and 13) at School 5. Using the .05 significance level, test whether the distribution of physically impaired students is different at different schools. Figure the chi-square for this data set yourself (round to two decimal places). What is the chi-square obtained?