Recall that "very satisfied" customers give the XYZ-Box video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of 64 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.   

(a) Letting µ represent the mean composite satisfaction rating for the XYZ-Box, set up the null hypothesis H₀ and the alternative hypothesis H_a needed if we wish to attempt to provide evidence supporting the claim that µ exceeds 42.

H₀: µ (Click to select)=≠≤><≥ 42 versus H_a: µ (Click to select)≥=>≤<≠ 42.

(b) The random sample of 64 satisfaction ratings yields a sample mean of x¯=42.970x¯=42.970. Assuming that σ equals 2.67, use critical values to test H₀ versus H_a at each of α = .10, .05, .01, and .001. (Round your answer z_.05 to 3 decimal places and other z-scores to 2 decimal places.)

z =      

Reject H₀ with α = (Click to select).001.10.10, .05, .01.01, .001 , but not with α =(Click to select).10.10, .05, .01.01, .001.001

(c) Using the information in part (b), calculate the p-value and use it to test H₀ versus H_a at each of α = .10, .05, .01, and .001. (Round your answers to 4 decimal places.)

(d) How much evidence is there that the mean composite satisfaction rating exceeds 42?

There is (Click to select)very strongextremely strongnoweakstrong evidence.

Provide formula for effect sizes and step-by-step solution by hand or software.

A researcher is studying the effects of inserting questions into instructional material for learning. There is doubt whether these questions would be more effective before or after the corresponding passage. In addition, the researcher wants to know the impact of factual and thought provoking questions. Students are randomly assigned to one of each of the four combination: position of question (before vs. after the passage) and type of question (factual vs. thought provoking). After 15 hours of studying under these conditions, the students are given a test on the content of the instructional materials. The test scores are below. What can be concluded with α = 0.01?

                     Position

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

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

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


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


d) Make an interpretation based on the results.

There is a question type difference in the test scores.There is no question type difference in the test scores.    

There is a question position difference in the test scores.There is no question position difference in the test scores.    

There is a question type by position interaction in the test scores.There is no question type by position interaction in the test scores.    

Given the data listed in the table, calculate the lower and upper bound for the 95% confidence interval for the mean at X = 7. The regression equation is given by y^ = b₀ + b₁x.

Give your answers to 2 decimal places. You may find this Student's t distribution table useful.

a) Lower bound =

b)Upper bound =

One generator is placed in standby redundancy to the main generator. The faliure rate of each generator is estimated to be λ = 0.05/hr. Compute the reliability of the system for 10 hrs and its MTBF assuming that the sensing and switching device is 100% reliable. If the reliability of this device is only 80%, how are the results modified?

PLEASE DO BY HAND AND NOT EXCEL

1.A car dealer believes that average daily sales for four different dealerships in four separate states are equal. A random sample of days results in the following data on daily sales:

Ohio                New York       West Virginia              Pennsylvania

               3                          10                         3                                  20

               2                            0                         4                                  11

               6                            7                         5                                  8

               4                            8                                                             2

               4                            0                                                             14

               7

               2

Use ANOVA to test this claim at the 0.05 level.

What does it mean to say that a particular result is statistically significant at the .05 level or at the .01 level? Is a result that is statistically significant at the .05 level automatically also significant at the .01 level? What about the reverse? Please explain your reasoning.

1.   Do consumers spend more on a trip to Walmart or Target? Suppose researchers interested in this question collected a systematic sample from 85 Walmart customers and 80 Target customers by asking customers for their purchase amount as they left the stores. The data collected are summarized in the table below.
   
Walmart
Target
sample size
85
80
sample mean
$45
$53
sample std dev
$20
$18

a.   Check the conditions to create a confidence interval for the difference in spending at the two stores.
b.   Create a 95% confidence interval for the difference in spending at the two stores. (Note: We don’t have the full data, so you can use the formulas on page 342 or a program that doesn’t require it.)
c.   Interpret your confidence interval with a sentence.
d.   Your CI from part b does not contain zero. Does that mean the difference in spending at the two stores is statistically significant? Why or why not?

We have:

                    P(A) = 0.75

                    P(B|A) = 0.9

                    P(B|A′) = 0.8

                    P(C|A ∩ B) = 0.8

                    P(C|A ∩ B′) = 0.6

                    P(C|A′ ∩ B) = 0.7

                    P(C|A′ ∩ B′) = 0.3     

Compute:

              a) ?(?′| ?′)

              b) P (?′ ∪ ?′)

              c) ?(? ∩ ? ∩ ?)

              d) P(C)

              e) ?(? ∩ ? ∩ ?)’

              f) P(B)

              g) P(AUBUC)

The life in hours of a thermocouple used in a furnace is known to be ap-

proximately normally distributed, with standard deviation

σ

= 20 hours. A

random sample of 15 thermocouples resulted in he following data: 553, 552,

567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529.

Use the 5 steps in the testing procedure to solve following question:

a) Is there evidence to support the claim that mean life exceeds 540 hours?

Use a fixed-level test with

α

= 0

.

05.

b) What is the P-value for this test?

c) Construct a 95% one-sided lower CI on the mean life.

d) Use the CI found above to test the hypothesis.

e) What is the β-value for this test if the true mean life is 560 hours?

PART 1.
A study reports the following final notation: F (2, 12) = 5.00, p > .05

a. How many samples were involved in this study?

b. How many total participants were involved in this study?

c. If MSwithin is 3, what is MSbetween?


PART 2.
Test the claim that the mean GPA for student athletes is higher than 3.1 at the .01 significance level.

Based on a sample of 50 people, the sample mean GPA was 3.15 with a standard deviation of 0.08

The test statistic is:  (to 3 decimals)

The p-value is:  (to 3 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 40 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.80 ml/kg for the distribution of blood plasma.

(a)

Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

lower limitupper limitmargin of error

(b)

What conditions are necessary for your calculations? (Select all that apply.)

the distribution of weights is uniformσ is knownn is largethe distribution of weights is normalσ is unknown

(c)

Interpret your results in the context of this problem.

1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.    The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

(d)

Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

male firefighters

Steve is the director of operations for a diamond company. The company is considering whether to launch a new product​ line, which will require building a new facility. The research required to produce the new product has not been proven to work in a​ full-scale operation. If Steve decides to build the new facility and the process is​ successful, the company will earn a profit of 720,000. If the process is​ unsuccessful, his company will realize a loss of 900,000. Steve estimates that the probability of the​ full-scale process succeeding is 62%. Steve has the option of constructing a pilot plant for 59,000 to test the new process before deciding to build the​ full-scale facility. He estimates there is a 54% probability that the pilot plant will prove successful. If the pilot plant succeeds he thinks the chance of the full scale facility succeeding is 87%. if the pilot plant fails, he thinks the chance of the full scale facility succeeding is only 35%. Complete parts a, b, and c below.

A.) Construct a decision tree with all of the known information labeled

B.) Advise what to do ( should he build the pilot plant first?)

C.) what is the most they should pay to construct the pilot plant?

A queuing system with a Poisson arrival rate and exponential service time has a single queue, two servers, an average arrival rate of 60 customers per hour, and an average service time of 1.5 minutes per customer.

The manager is thinking of implementing additional queues to avoid an overloaded system. What is the minimum number of additional queues required? Explain.

How many additional servers are required to ensure the utilization is less than or equal to 50%? Explain.

If the manager loses a server, what service time would be necessary to ensure that the queue length is not at risk of approaching infinity? Explain.

PLEASE DO BY HAND AND NOT EXCEL

1. Suppose we have the following data on variable X (independent) and variable Y (dependent):

X         Y

2          70

0          70

4          130

a. Test to see whether X and Y are significantly related using a t-test on the slope of X. Test this at the 0.05 level.

b. Test to see whether X and Y are significantly related using an F-test on the slope of X. Test this at the 0.05 level.