A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below. 28 18 15 20 14 25 21 29 20 23 24 26 It is known that the population standard deviation is 6. The instructor has recommended that students devote 2 hours per week for the duration of the 12-week semester, for a total of 24 hours.

Test to determine whether there is evidence at the 0.01 significance level that the average student spent less than the recommended amount of time. Fill in the requested information below.

A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a) is expressed (-infty, a), an answer of the form (b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value

D. Your decision for the hypothesis test

Reject H0

Do Not Reject H1

Reject H1

Do Not Reject H0.

In the 2015 federal election, 39.5% of the electorate voted for the Liberal party, 31.9% for the Conservative party, 19.7% for the NDP, 4.7% for the Bloc Quebecois and 3.5% for the Green party.

The most recent pool as of the launch of the 2019 election campaign shows a tie between the Liberals and the Conservatives at 33.8%. This pool was based on 1185 respondents. (a) Based on this recent pool, test whether this is sufficient evidence to conclude that the level of support for the conservatives has increased since the last election. Use the 5% level of significance and show your manual calculations. (b) Using recent pool data, build an appropriate 95% one-sided confidence interval for the true proportion of support for the conservatives. Is this CI consistent with your conclusion in a) above? (c) Would your conclusion be the same as in a) above if you had used a 10% confidence level for the hypothesis test? (d) Now, suppose you want to estimate the national level of support for the Liberals at the start of the 2019 campaign using a 95% 2-sided confidence interval with a margin of error of  1% based on the results of the last election, what sample size would be required? (e) Would the sample size calculated above be sufficient to estimate the support for the Bloc Quebecois within the same level of confidence and margin of error? If not, how many more respondents would you need?

The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four explanatory variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table.

a. For each explanatory variable, discuss whether it is likely to have a positive or negative causal effect on time until the first engine overhaul.

The effect on time is either Positive or Negative! Fill them in below.

b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

TimeˆTime^  = ________+_______ Miles +_______ Load + ________ Speed + _______ Oil

c. Based on part (a), are the signs of the regression coefficients logical?
The below signs will be filled with the word logical or not logical!

d. What is the predicted time before the first engine overhaul for a particular truck driven 57,000 miles per year with an average load of 18 tons, an average driving speed of 57 mph, and 18,000 miles between oil changes. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Excel data:

Don't care how you solve as long as answers are correct. I will like for it being correct!

10.4: Inferences About the Difference Between Two Population Proportions

In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded.

Use and test the hypothesis that there is no difference in the recall proportions for the two commercials.

Formulate the null and the alternative hypotheses.

- Select your answer -greater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0Item 1

- Select your answer -greater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0Item 2

What is the value of the test statistic (to 2 decimals)?

What is the -value (to 4 decimals)?

Does there appear to be a difference in recall proportions for the two commercials?

- Select your answer -NoYesItem 5

Compute a confidence interval for the difference between the recall proportions for the two populations (to 4 decimals).

( , )

It appears that - Select your answer -Commercial ACommercial Bneither commercial item 8 has a better recall rate.

Use and test the hypothesis that there is no difference in the recall proportions for the two commercials.

Formulate the null and the alternative hypotheses.

- Select your answer -greater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0

- Select your answer -greater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0

What is the value of the test statistic (to 2 decimals)?

What is the -value (to 4 decimals)?

Does there appear to be a difference in recall proportions for the two commercials?

- Select your answer -NoYes

Compute 95 % a confidence interval for the difference between the recall proportions for the two populations (to 4 decimals).

( ______, ______)

It appears that - Select your answer -

Commercial A

Commercial B

neither Commercial

Commercial none

Imagine you are in charge of a program in which members are evaluated on five different tests at the end of the program. Why doesn't it make sense to simply compute the average of the five scores as a measure of performance rather than compute a z score for each test for each individual and average those?

Good performance (obtaining a grade of A+) in this probability class depends on your attendance (A) and completion of assignments (C). The probability that you will receive a grade of A+ are 95%, 75%, 50%, and 0%, if you attend the class and complete the assignments, if you attend but do not complete assignments, if you do not attend but complete assignments, and if you neither attend nor complete assignments, respectively. Further assume that if you attend the class, there is a 90% probability that you will complete the assignments. The probability that you will attend the class is 0.95 and the probability that you will complete the assignments is 0.90.

(a) What is the probability that you will receive an A+ in this class?

(b) If a student receives an A+, what is the probability that you attend the class and completed the assignments?

In psychology, there is a particular Mental Development Index (MDI) used in the study of infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. We are going to randomly select 64 children and average their MDI scores. What is the probability that the average is greater than 102?

16. A process engineer at Sival Electronics was trying to determine whether three suppliers would be equally capable of supplying the mounting boards for the new “gold plated” components that she was testing. The Ch05Data.xlsx file for Prob05-16 on the Student Companion Site shows the coded defect levels for the suppliers, according to the finishes that were tested. Lower defect levels are preferable to larger levels. Using one-way ANOVA, analyze these results. What conclusion can be reached, based on these data?

14. Softswift, a software developer, is trying to determine if any of three potential subcontractors has better programmers in order to outsource a development project. The three subcontractors agreed to test five pro-grammers, using a standardized test provided by Softswift, as provided in the data in the Ch05Data.xlsx Excel workbook file for Prob05-14. Use the single factor ANOVA Excel tool to determine if there is a significant dif-ference between the scores of programmers at the three contractors at the 5 percent level.

***PLEASE SHOW HOW TO SOLVE IN EXCEL*** NOT HANDWRITTEN

5) The letter grades on the midterm exam given in a large managerial statistics class are normally distributed with mean 75 and standard deviation 9. The instructor of this class wants to assign an A grade to the top 10% of the scores, a B grade to the next 10% of the scores, a C grade to the next 10% of the scores, a D grade to the next 10% of the scores and an F grade to all scores below the 60th percentile of this distribution. For each possible letter grade, find the lowest acceptable score.

A manufacturer of TV sets claims that at least 98% of its TV sets can last more than 10 years without needing a single repair. In order to verify and challenge this claim, a consumer group randomly selected 800 consumers who had owned a TV set made by this manufacturer for 10 years. Of these 800 consumers, 60 said that their TV sets needed some repair at least once. a. Is there significant evidence showing that the manufacturer’s claim is false? Test using α = 0.01. b. Do the data support that the manufacturer’s actual no-repair rate does not even reach 94%? Use α = 0.01. need to know how the variance is found step by step

c. Explain the concept of ANOVA, and say how you can conduct an ANOVA analysis for the wages/salaries of three categories of workers in your firm. Use an example to illustrate. Clearly indicate the F-Statistic and the Critical Value and their meanings

1. Determine the following probabilities and for each item, provide a sketch of the associated areas (3 points each).

a. P(z > 1.69)

b. P(z < -2.03)

c. P(z > -0.50)

d. P(-0.39 < z < 0)

e. P(0.75 < z < 2.01)

You may need to use the appropriate technology to answer this question.

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

x₁

and

x₂.

The estimated regression equation for these data is

ŷ = −18.21 + 2.01x₁ + 4.72x₂.

Here, SST = 15,134.9, SSR = 13,994.6,

s_b1 = 0.2482,

and

s_b2 = 0.9524.

(a)

Test for a significant relationship among

x₁, x₂, and y.

Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ > β₂
H_a: β₁ ≤ β₂H₀: β₁ = β₂ = 0
H_a: One or more of the parameters is not equal to zero.     H₀: β₁ ≠ 0 and β₂ ≠ 0
H_a: One or more of the parameters is equal to zero.H₀: β₁ ≠ 0 and β₂ = 0
H_a: β₁ = 0 and β₂ ≠ 0H₀: β₁ < β₂
H_a: β₁ ≥ β₂

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.     Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.Reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.

(b)

Is

β₁

significant? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ < 0
H_a: β₁ ≥ 0     H₀: β₁ > 0
H_a: β₁ ≤ 0H₀: β₁ = 0
H_a: β₁ > 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that β₁ is significant.Reject H₀. There is insufficient evidence to conclude that β₁ is significant.     Do not reject H₀. There is sufficient evidence to conclude that β₁ is significant.Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant.

(c)

Is

β₂

significant? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₂ < 0
H_a: β₂ ≥ 0H₀: β₂ > 0
H_a: β₂ ≤ 0     H₀: β₂ ≠ 0
H_a: β₂ = 0H₀: β₂ = 0
H_a: β₂ ≠ 0H₀: β₂ = 0
H_a: β₂ > 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that β₂ is significant.Do not reject H₀. There is sufficient evidence to conclude that β₂ is significant.     Do not reject H₀. There is insufficient evidence to conclude that β₂ is significant.Reject H₀. There is insufficient evidence to conclude that β₂ is significant.

The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals who are in marketing. Three groups are considered: management, research and advertising (higher scores indicate higher ethical values).

1. Compute the values identified below (to 1 decimal, if necessary).
   

   Sum of Squares, Treatment
   Sum of Squares, Error
   Mean Squares, Treatment
   Mean Squares, Error

   
   
2. Use  = .05 to test for a significant difference in perception among the three groups.
   
   Calculate the value of the test statistic (to 2 decimals).
     
   
   The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6  
   
   What is your conclusion?
   SelectConclude the mean perception scores for the three groups are not all the sameCannot conclude there are differences among the mean perception scores for the three groupsItem 7  
   
3. Using  = .05, determine where differences between the mean perception scores occur.
   
   Calculate Fisher's LSD value (to 2 decimals).
     
   
   Test whether there is a significant difference between the means for marketing managers (1), marketing research specialists (2), and advertising specialists (3).
   

   Difference	Absolute Value	Conclusion
   1 -  2		SelectSignificant differenceNo significant differenceItem 10
   1 -  3		SelectSignificant differenceNo significant differenceItem 12
   2 -  3		SelectSignificant differenceNo significant differenceItem 14