9. As part of a study of corporate employees, the director of human resources for PNC Inc. wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month. The population standard deviations for the Cincinnati and Pittsburgh employees are 30 and 26 miles, respectively. By following the six-step procedure for hypothesis testing found below, answer the following: At the 0.05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees?

Step 1: State the Null Hypothesis (H_0) and the Alternate Hypothesis (H_1)

Step 2: Determine the level of significance. (Note: It’s given in this problem!)

Step 3: Select the Test Statistic

Step 4: Formulate the Decision Rule

Step 5: Make a Decision

Step 6: Interpret the Result

In a poll of

593

human resource​ professionals,

49.1

​%

said that body piercings and tattoos were big grooming red flags. Complete parts​ (a) through​ (d) below.

​a) Among the

593

human resource professionals who were​ surveyed, how many of them said that body piercings and tattoos were big grooming red​ flags?

291

​(Round to the nearest integer as​ needed.)

​b) Construct a​ 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags.

0.438

less than p less than0.544

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

​c) Repeat part​ (b) using a confidence level of​ 80%.

_____<p< _________

The Super-warm Company produces two electric heaters (products A and B) that require both heating elements and electrical components. The owner currently determines how many units of each product to be produced so as to maximize the profit. For each unit of product A, 3 units of heating elements and 1 unit of electrical components are required. For each unit of product B, 1 unit of heating elements and 2 units of electrical components are required. The company has 750 units of heating elements and 600 units of electrical components. Each unit of product A, up to 130 units, gives a profit of $30, and each unit of product B gives a profit of $20. Any excess over 130 units of product A brings no extra profit, so such an excess has been ruled out.

a) Formulate a Linear Programming model for this problem.

b) Use the graphical method to solve this model. What is maximum total profit?

A college dean is interested in the exam performance of students in a biology course. After the final exam, students are randomly selected from three different section of the biology course. What can be conclude with an α of 0.05? The data are below.

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.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

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

d) Make an interpretation based on the results.

At least on section differs on the final exam.None of the sections differ on the final exam.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 2: difference =  ; significant:  ---Select--- Yes No
2 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes No

An educational psychologist has developed a mediation technique to reduce anxiety. The psychologist selected a sample of high anxiety students that are asked to do the mediation at two therapy sessions a week apart. The participants' anxiety is measured the week before the first session and at each subsequent session. Below are the anxiety scores for the participants. What can the psychologist conclude with α = 0.01?

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.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

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

d) Make an interpretation based on the results.

At least one of the sessions differ on anxiety.None of the sessions differ on anxiety.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =  ; significant:  ---Select--- Yes No
2 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

Consider the following data for a dependent variable y and two independent variables, x₁and x₂.

Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary.

a. Develop an estimated regression equation relating y to x₁.

ŷ =  +  x₁

Predict y if x₁= 35.

ŷ =

b. Develop an estimated regression equation relating y to x₂.

ŷ =  +  x₂

Predict y if x₂= 25.

ŷ =

c. Develop an estimated regression equation relating y to x₁and x₂.

ŷ =  +  x1 +  x2

Predict y if x₁= 35 and x₂= 25.

ŷ =

A personnel director in a particular state claims that the mean annual income is greater in one of the​ state's counties​ (county A) than it is in another county​ (county B). In County​ A, a random sample of 1818 residents has a mean annual income of $ 40 comma 800$40,800 and a standard deviation of $ 8500$8500. In County​ B, a random sample of 88 residents has a mean annual income of $ 37 comma 700$37,700 and a standard deviation of $ 5500$5500. At alphaαequals=0.100.10​, answer parts​ (a) through​ (e). Assume the population variances are not equal. If​ convenient, use technology to solve the problem.

When using r programming or statistical software:

(A) From the summary, which variables seem useful for predicting changes in independent variable?

(B) For the purpose of variable selection, does the ANOVA table provide any useful information not already in the summary?

Why is it popular for advertisements to always state a confidence interval? Give an example of where you have seen this.

For small training sets variance may contribute more to the overall error than bias. Sometimes this is handled by reducing the complexity of the model, even if the model is too simple. Why do you suppose this is the case? Come up with your own example of this

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years.

To make sure the Excel regression package is installed.

Click “Tools”, à“Add-Ins” àchoose “Analysis Toolpak” and click “OK”.

To use the Excel regression package,                                                     

Click “Tools”, à“Data Analysis” and click “Regression”.

            a.   Use the method of least squares to compute an estimated regression line between sales and advertising.

            b.   If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.

            c.   What does the slope of the estimated regression line indicate?

            d.   What is the coefficient of determination and fully interpret its meaning.

            e.  What is the standard error of the estimation?

            f.    Use the F test to determine whether or not the regression model is significant at a= 0.05.

            g.   Use the t test to determine whether the slope of the regression model is significant at a= 0.05.

            h.   Develop a 99% confidence interval for the slope of the regression model.

The prices of the 21​ top-rated 28-inch direct view television sets are as follows. ​$340 ​$410 ​$510 ​$620 ​$710 ​$810 ​$860 360 430 550 620 750 810 890 380 470 580 660 780 840 890 Determine Upper Q 2​, Upper Q 1​, and Upper Q 3.

Find the value of the standard normal random variable zz , called z0z0 such that:

(a) P(z≤z0)=0.9999P(z≤z0)=0.9999
z0=z0=

(b) P(−z0≤z≤z0)=0.922P(−z0≤z≤z0)=0.922
z0=z0=

(c) P(−z0≤z≤z0)=0.3954P(−z0≤z≤z0)=0.3954
z0=z0=

(d) P(z≥z0)=0.4497P(z≥z0)=0.4497
z0=z0=

(e) P(−z0≤z≤0)=0.3225P(−z0≤z≤0)=0.3225
z0=z0=

(f) P(−1.66≤z≤z0)=0.5474P(−1.66≤z≤z0)=0.5474
z0=z0=

The manager of a supermarket chain wants to determine if the location of the product - where it is to be displayed - has any effect on the sale of a pet toys. Three different aisle locations are to be considered: the front of the aisle, the middle of the aisle, or the rear-aisle. Twenty-one stores are randomly selected, with 7 stores randomly assigned to sell the pet toy at the front-aisle, the middle-aisle, and the rear-aisle.

Front Middle Rear

8.6 3.2 4.6 7.2 2.4 6.0 5.4 2.0 4.0 6.2 1.4 2.8 5.0 1.8 2.2 4.0 1.6 2.8 4.5 1.8 2.5

A boxplot of the data is provided as well as MINITAB output:

1. (a) Does this data indicate that the sales of the pet toy are the same at the three aisle locations? State the appropriate statistical hypotheses.

2. (b) To test the H0 in part (a), an ANOVA table was obtained in MINITAB:

        Source  DF     SS     MS      F      P
        Factor   2  51.59
        Error
        Total   20  80.82
   

   The P-value of test was found to be 0.000106.
   (i) Provide the value of the test statistic from which this P -value was found.

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.6

(ii) Using a level of significance of 5%, what can you conclude from this data? Write a brief sentence describing your finding. [2]

(c) The output below results from an application of Tukey’s HSD method.

   Front subtracted from:

            Lower  Center   Upper   --+---------+---------+---------+-------
   Middle  -5.553  -3.814  -2.076   (------*------)
   Rear    -4.024  -2.286  -0.547         (------*------)

                                    --+---------+---------+---------+-------
                                   -5.0      -2.5       0.0       2.5

   Middle subtracted from:

          Lower  Center  Upper   --+---------+---------+---------+-------
   Rear  -0.210   1.529  3.267                        (------*------)

Summarize these results.

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.4

MINITAB output:

Pearson correlation of MATScore and CalculusGrade = 0.840
Coefficients

Term       Coef  SD Coef  T-Value  P-Value
Constant  40.78     8.51     4.79    0.001
MATScore  0.766    0.175     4.38    0.002

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.5

1. (a) From the scatterplot, what can you say about the relationship between a student’s math achievement

   test score and their Calculus I final grade?

2. (b) Letting a student’s math achievement test score be the predictor variable x and their Calculus I final grade by the response variable y, estimate the model that allows you to predict a student’s Calculus I final grade as a linear function of his/her math achievement test score.

3. (c) Find the coefficient of determination, and interpret its meaning.

4. (d) Does the data indicate that the y-intercept of the model can be removed or retained? Use a level of significance of 5%.

5. (e) Find a 95% confidence interval estimate for β1, and interpret its meanign. (Note: t0.025,df=8 = 2.306).

6. (f) Consider the following MINITAB output:

        Variable  Setting
        MATScore       70
   

            Fit   SE Fit        95% CI              95% PI
        94.3735  5.02118  (82.7946, 105.952)  (71.2024, 117.545)
   

   Find a 95% confidence interval that will predict the Calculus I final grade of a student who scored 70% on their math achievement test score.