only 2 questions

((PLSS with steps and clear hand written PLSSS and thank you sooooo much for helping me))

Depression	Geographic location	Gender
3	Florida	Female
7	Florida	Male
7	Florida	Female
3	Florida	Female
8	Florida	Female
8	Florida	Male
8	Florida	Male
5	Florida	Female
5	Florida	Male
2	Florida	Female
6	Florida	Female
2	Florida	Female
6	Florida	Female
6	Florida	Male
9	Florida	Female
7	Florida	Male
5	Florida	Male
4	Florida	Male
7	Florida	Female
3	Florida	Female
8	New York	Female
11	New York	Male
9	New York	Male
7	New York	Male
8	New York	Female
7	New York	Male
8	New York	Female
4	New York	Male
13	New York	Female
10	New York	Male
6	New York	Female
8	New York	Female
12	New York	Female
8	New York	Male
6	New York	Male
8	New York	Male
5	New York	Male
7	New York	Female
7	New York	Male
8	New York	Male
10	North Carolina	Male
7	North Carolina	Female
3	North Carolina	Male
5	North Carolina	Male
11	North Carolina	Female
8	North Carolina	Female
4	North Carolina	Male
3	North Carolina	Male
7	North Carolina	Female
8	North Carolina	Male
8	North Carolina	Female
7	North Carolina	Female
3	North Carolina	Female
9	North Carolina	Female
8	North Carolina	Female
12	North Carolina	Female
6	North Carolina	Male
3	North Carolina	Male
8	North Carolina	Male
11	North Carolina	Female

As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location, gender and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. The data collected follow; higher test scores indicate higher levels of depression.

........

h) Is there any significant difference of the mean of depression value due to geographic location? Use a 0.05 level of significance.

i) Give point estimates for the proportion of individuals according to their gender.

I was given this problem:

PART A:

Consider the following model of wage determination:

wage= 0+1educ+2exper+3married+ε

where:    wage = hourly earnings in dollars

    educ = years of education

    exper = years of experience

    married = dummy equal to 1 if married, 0 otherwise

Using data from the file ps2.dta, which contains wage data for a number of workers from across the United States, estimate the model shown above by OLS using the regress command in Stata. As always, be sure to include your Stata output (show the regression command used and the complete regression output).

Why are we unable to determine which of the included variables is the most important determinant of wages by simply looking at the size (and perhaps significance) of the estimated coefficients (even if we were confident that these estimates reflected unbiased causal impacts)?

My answer to PART A:

. regress wage educ exper married

     Source |       SS df       MS Number of obs  = 526

-------------+----------------------------------   F(3, 522) = 54.97

      Model |  1719.00074         3 573.000246 Prob > F        = 0.0000

   Residual |  5441.41355     522 10.4241639 R-squared       = 0.2401

-------------+----------------------------------   Adj R-squared = 0.2357

      Total |  7160.41429       525 13.6388844 Root MSE        = 3.2286

------------------------------------------------------------------------------

       wage |    Coef. Std. Err.      t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

       educ | .6128507   .0542332 11.30 0.000     .5063084 .7193929

      exper |   .0568845 .0116387     4.89 0.000 .0340201     .079749

    married |   .9894464 .309198     3.20 0.001 .3820212    1.596872

      _cons |  -3.372934   .7599027 -4.44   0.000 -4.865777 -1.880091

We are unable to determine which of the independent variables is the strongest predictor of wage because the predictors use different units of measurement.

Is this answer correct?

PART B:

Estimate the model again in Stata, but now include the “beta” option and explain how the additional information provided helps to provide insight into this issue discussed in part (c). As part of your answer, provide a clear interpretation of the new Stata output corresponding to the educ variable.  

My answer to PART B:

The “, beta” command, shows us the standardized coefficients and enables us to make a comparison of the independent variables’ relationship to the dependent variable; the higher the absolute value of the beta coefficient for each the independent variable, the stronger predictor it is of the dependent variable. The beta coefficient shows how one unit change in the independent variable’s standard deviation corresponds to a change in the standard deviation of the dependent variable. From the STATA output, are able to see that educ has the highest beta coefficient, meaning that education is the strongest predictor of wage. Whether or not someone is married is the weakest predictor of wage.

regress wage educ exper married, beta

     Source |       SS df       MS Number of obs  = 526

-------------+----------------------------------   F(3, 522) = 54.97

      Model |  1719.00074         3 573.000246 Prob > F        = 0.0000

   Residual |  5441.41355     522 10.4241639 R-squared       = 0.2401

-------------+----------------------------------   Adj R-squared = 0.2357

      Total |  7160.41429       525 13.6388844 Root MSE        = 3.2286

------------------------------------------------------------------------------

       wage |    Coef. Std. Err.      t P>|t|        Beta

-------------+----------------------------------------------------------------

       educ | .6128507   .0542332 11.30 0.000                 .4595065

      exper |   .0568845 .0116387     4.89 0.000     .2090517

    married |   .9894464 .309198     3.20 0.001     .1308998

      _cons |  -3.372934   .7599027 -4.44   0.000         .

Is my answer correct?

Calculate the sample standard deviation and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Heart Rates in Beats per MinuteClass Frequency 61 - 66 12 67 - 72 3 73 - 78 9 79 - 84 11 85 - 90 13

Ten measurements of impact energy on specimens of A238 steel at 60 ºC are as follows: 64.1, 64.7, 64.5, 64.6, 64.5, 64.3, 64.6, 64.8, 64.2, and 64.3 J.

a. Use the Student’s t distribution to find a 95% confidence interval for the impact energy of A238 steel at 60 ºC.

b. Use the Student’s t distribution to find a 98% confidence interval for the impact energy of A238 steel at 60 ºC.

Life expectancy in the US varies depending on where an individual lives, reflecting social and health inequality by region. You are interested in comparing mean life expectancies in counties in California, specifically San Mateo County and San Francisco County. Given the data below, answer the following questions.

	Mean life expectancy at birth for males in 2014	Sample standard deviation	Sample size (n)
San Mateo County	81.13 years	8.25	101
SF County	79.34 years	9.47	105

1. Calculate the standard error of the mean difference in male life expectancy between the 2 counties, assuming nonequal variance.

2. Calculate a 99% confidence interval for the mean difference in male life expectancy between the two counties. Use the conservative approximation for degrees of freedom.

3.Based on your confidence interval, would you expect the mean difference in male life expectancy to be statistically significant at the α=.01 level? EXPLAIN

B.38  

Average Size of a Performing Group in the Rock and Roll Hall of Fame

From its founding through 2015, the Rock and Roll Hall of Fame has inducted 303 groups or individuals, and 206 of the inductees have been performers while the rest have been related to the world of music in some way other than as a performer. The full dataset is available at RockandRoll on StatKey. Some of the 206 performer inductees have been solo artists while some are groups with a large number of members. We are interested in the average number of members across all groups or individuals inducted as performers.

(a)  

What is the mean size of the performer inductee groups (including individuals)? Use the correct notation with your answer.

(b)  

Use technology to create a graph of all 206 values. Describe the shape, and identify the two groups with the largest number of people.

(c)  

Use technology to generate a sampling distribution for the mean size of the group using samples of size n = 10. Give the shape and center of the sampling distribution and give the standard error.

(d)  

What does one dot on the sampling distribution represent?

If the moment-generating function of X is M(t) = exp(3 t + 12.5 t²) = e^{3 t + 12.5 t2}.

a. Find the mean and the standard deviation of X.

Mean =

standard deviation =

b. Find P(4 < X < 16). Round your answer to 3 decimal places.

c. Find P(4 < X² < 16). Round your answer to 3 decimal places.

11.A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.5 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you support the organization’s claim using the test statistic?

Claim is alternative, reject the null and support claim as test statistic (-2.66) is in the rejection region defined by the the critical value (-2.05)

Claim is alternative, fail to reject the null and cannot support claim as test statistic (-2.66) is in the rejection region defined by the critical value (-2.05)

Claim is null, reject the null and support claim as test statistic (-2.66) is in the rejection region defined by the critical value (-2.05)

Claim is null, fail to reject the null and cannot support claim as test statistic (-2.66) is in the rejection region defined by the critical value (-2.05)

12. A pharmaceutical company claims that the average cold lasts an average of 8.4 days. They are using this as a basis to test new medicines designed to shorten the length of colds. A random sample of 106 people with colds, finds that on average their colds last 8.28 days. The population is normally distributed with a standard deviation of 0.9 days. At α=0.02, what type of test is this and can you support the company’s claim using the p-value?

Claim is null, reject the null and cannot support claim as the p-value (0.170) is less than alpha (0.02)

Claim is null, fail to reject the null and support claim as the p-value (0.170) is greater than alpha (0.02)

Claim is alternative, fail to reject the null and support claim as the p-value (0.085) is less than alpha (0.02)

Claim is alternative, reject the null and cannot support claim as the p-value (0.085) is greater than alpha (0.02)

13. A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.77 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim?

No, since p>α, we reject the null and the null is the claim

No, since p>α, we fail to reject the null and the null is the claim

Yes, since p>α, we fail to reject the null and the null is the claim

Yes, since p<α, we reject the null and the null is the claim

14. The company’s cleaning service states that they spend more than 46 minutes each time the cleaning service is there. The company times the length of 37 randomly selected cleaning visits and finds the average is 47.2 minutes. Assuming a population standard deviation of 5.2 minutes, can the company support the cleaning service’s claim at α=0.10?

Yes, since p>α, we reject the null. The claim is the null, so the claim is not supported

Yes, since p<α, we fail to reject the null. The claim is the null, so the claim is not supported

No, since p>α, we fail to reject the null. The claim is the alternative, so the claim is not supported

No, since p<α, we reject the null. The claim is the alternative, so the claim is supported

15.. A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.26 minutes. The population standard deviation is assumed to be 0.29 minutes. Can the claim be supported at α=0.08?

No, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported

Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported

Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported

No, since test statistic is not in the rejection region defined by the critical value, fail to reject the null. The claim is the alternative, so the claim is not supported

3.For variables measured at the nominal level, what values can the measures of association take on? What about variables at the ordinal and interval/ratio levels?

Does pollution increase mean death rate? A researcher sampled 31 “unpolluted” areas greater than 50 km away from industrial plants, and 23 different “polluted” areas near industrial plants. The average mortalities in the unpolluted areas were 3 deaths per day per 100000 people (with a sample standard deviation of 0.4 deaths/day/100000 people), and was 3.3 deaths per day per 100000 people (with a sample standard deviation of 0.5 deaths/day/100000 people) in the polluted area. At the alpha=0.01 level, answer the question does pollution increase average death rate? Show statistical and critical values as appropriate. Assume that variances are equal.

  You are studying the relationship between smoking and hair loss. You find a positive moderate effect size. You conclude:

	A.	there is clinical significance
	B.	the correlation between smoking and hair loss is between -0.3 and -0.5
	C.	the correlation between smoking and hair loss is between 0.3 and 0.5
	D.	this is a significant relationship

A tax auditor is selecting a sample of 5 tax returns for an audit. If 2 or more of these returns are​"improper," the entire population of 50 tax returns will be audited. Complete parts​ (a) through​ (e) below.

Q. What is the probability that the entire population will be audited if the true number of improper returns in the population is:

a) 15

b) 20

c) 5

d) 10

Review these Skill Builders (and all of the other Course Materials): -Evaluating p-values -Statistical Power Identify the scenario you are evaluating and name the population. Estimate the size of that population. Example: the population of scenario 1 seems to be students at a State University so you could estimate the number of students at a typical State University. The University of South Florida up the road from me has about 40,000 students Identify the independent variable (IV) and the dependent variable (DV). Sometimes this is stated by the researchers and sometimes you have to ferret it out. In scenario 2, the IV and DV are given as Race and Education, respectively. Write a null hypothesis. If the null hypothesis is not provided in the scenario, write a null hypothesis based on the information that is provided in the scenario. Each scenario addresses differences in an interval or ratio DV among a Nominal or Ordinal IV made up of 2 or more groups. So write the null hypothesis this way: There is no difference in Education based on Race among (state/name the population). Critically evaluate the sample size. This is tricky because the scenarios do not provide us with the right information to calculate an appropriate sample size. And you want to avoid stating that a sample size ‘seems’ to be the right size (very amateurish). What to do? Go to this sample size calculator: https://www.surveysystem.com/sscalc.htm. Use the box labeled Calculate Sample Size, Enter .95 for the confidence level, your estimate of the population, 5 for the confidence interval and see what pops up for the ideal sample size. Compare that number to the sample size in the scenario and critically evaluate the sample size in terms of making a Type I or Type II error. For example, if the sample size is smaller than the ideal sample size, does the probability of making a Type I error increase or decrease. Do the same drill with a Type II error. Critically evaluate the scenario for meaningfulness. Follow the guidance I provided in the Announcement Week 5 Discussion: How To Critically Evaluate The Discussion Scenario. Note: we can often relate meaningfulness to social change. That is, if the research is meaningful then it may have implications for social change. Try evaluating meaningfulness and social change in the same paragraph. But first, define meaningfulness and define social change. Cite, cite, cite. Critically evaluate the statements for statistical significance. Compare the researcher reported p-value for the hypothesis test they conducted (either a t-test or an ANOVA) to the confidence level (usually .05). If the reported p-value is greater than .05, then the researcher should fail to reject the null hypothesis and state that there is no statistical significance. If the reported p-value is less than .05, then the researcher should reject the null hypothesis and state that there is statistical significance. I know this is counter-intuitive. Just do it. Add this for grins, “There is no such decision as ‘rapidly approaching significance.’ This is statistics, not a hurricane watch.” Select 1 response to the following multiple choice question: What scenario would you find to be the least fun?Having a root canal performed by an experienced dentist. Having 4 root canals performed by an unsupervised novice dentist. Having 21 root canals performed by a trained Capuchin monkey. Trying to statistically determine differences in patient post-root canal pain levels based on the dentist’s training.

A researcher wants to test whether the mean lengths of two species of trout are the same. He obtains the weights of 10 individuals of species A and 10 individuals of species B. The sample mean weights are 12.3 kg and 14.3 kg, respectively, and the sample variances are 3.5 kg² and 4.5kg². Assume that the lengths are normally distributed.  

a. Should we retain the hypothesis that the population variances are equal?

b. Should we retain the hypothesis that the population means are equal?

The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars.

Predictor	Coef	SE Coef	T	P
Constant	7.987	2.967	2.69	-
X1	0.12242	0.03121	3.92	0.0000
X2	-0.12166	0.05353	-2.27	0.028
X3	-0.06281	0.03901	-1.61	0.114
X4	0.5235	0.1420	3.69	0.001
X5	-0.06472	0.03999	-1.62	0.112
Analysis of Variance
Source	DF	SS	MS	F	P
Regression	5	3710.00	742.00	12.89	0.000
Residual Error	46	2647.38	57.55
Total	51	6357.38

X1 - # of architects employed by the company

X2 - # of engineers employed by the company

X3 - # of years involved with health care projects

X4 - # of states in which the firm operates

X5 - % of the firms work that is health care-related

1. Write out the regression equation
2. How large is the sample? How many independent variables are there?
3. Conduct a global test of hypothesis to see if any of the set of regression coefficients could be different from 0. Use the .05 significance level. What is your conclusion?
4. Conduct a test of hypothesis for each independent variable. Use the .05 significance level. Which variable would you consider eliminating first?
5. Outline a strategy for deleting independent variables in this cas