9 statistics questions 1

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.

3 7 8 9 10 10 10 9 9 9 9 8 5
6 7 7 9 8 10 9 8 7 6 8 7 9
5 3 9 10 10 9 9 8 9 8 6 10 8
4 7 3 10 8 9 8 10 10 8 8

Develop a 95% confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.



Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.)

Suppose a random sample of size 53 is selected from a population with σ = 9. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

a. The population size is infinite (to 2 decimals).


b. The population size is N = 50,000 (to 2 decimals).


c. The population size is N = 5000 (to 2 decimals).


d. The population size is N = 500 (to 2 decimals).


The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.28, 0.2, 0.2, 0.13, and 0.19.

  1. Show the probability distribution for the expense forecast.
    x f(x)
    9

    10

    11

    12

    13

  2. What is the expected value of the expense forecast for the coming year (to 2 decimals)?


  3. What is the variance of the expense forecast for the coming year (to 2 decimals)?


  4. If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)?


A simple random sample of 700 individuals provides 100 Yes responses.

a. What is the point estimate of the proportion of the population that would provide Yes responses (to 2 decimals)?


b. What is your estimate of the standard error of the proportion (to 4 decimals)?


c. Compute the 95% confidence interval for the population proportion (to 4 decimals).
(


,


)

America’s young people are heavy Internet users; 87% of Americans ages 12 to 17 are Internet users (The Cincinnati Enquirer, February 7, 2006). MySpace was voted the most popular website by 9% in a sample survey of Internet users in this age group. Suppose 1,600 youths participated in the survey. What is the margin of error, and what is the interval estimate of the population proportion for which MySpace is the most popular website? Use a 95% confidence level and round your answers to 3 decimals. For interval estimate Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.)

Margin error =

Interval estimate =

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.

Distance to Work Number of Days Absent
1 7
3 4
4 7
6 6
8 5
10 2
12 5
14 1
14 4
18 1
  1. Which of the following scatter diagrams accurately represents these data?
  2. Scatter Diagram #1



    Scatter Diagram #2



    Scatter Diagram #3




  3. Consider the following three scatter diagrams of the residuals against the independent variable. Which of the following accurately represents the data?

    Scatter Diagram #1
    Scatter Diagram #2Scatter Diagram #3



  4. Develop the least squares estimated regression equation (to 3 decimals).
    Days Absent =


    +


    Distance
  5. Is there a significant relationship between the two variables? Use
    = .05.

    Compute the value of the F test statistic (to 2 decimals).


    The p-value is



    What is your conclusion?



  6. What is the value of r2 (to 3 decimals)? Note: report r2 between 0 and 1.


  7. Did the estimated regression equation provide a good fit?



  8. Use the estimated regression equation developed in part (c) to develop a 95% confidence interval for the expected number of days absent for employees living 5 miles from the company (to 1 decimal).
    (


    ,


    )

When a new machine is functioning properly, only 7% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.

a. Using the Figure 5.3, select a tree diagram that shows this problem as a two-trial experiment. Here D: defective; G: not defective.

1.
2.
3.
4.

Choose the Correct option from the above tree diagrams:



b. How many experimental outcomes result in exactly one defect being found?


c. Compute the probabilities associated with finding no defects, exactly one defect, and two defects (to 4 decimals).

P (no defects)

P (1 defect)

P (2 defects)

Consider the following hypothesis test:

H0: μ ≤ 50

Ha: μ > 50

A sample of 60 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use α = .05.

a. With x = 52.5, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?



b. With x = 51, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?



c. With x = 51.8, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?



In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005).

  1. In a sample of 7 workers, what is the probability that exactly three workers take public transportation daily (to 4 decimals including interim calculations)?


  2. In a sample of 7 workers, what is the probability that at least three workers take public transportation daily (to 4 decimals including interim calculations)?


The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows.

Brand Price Score
Bose 180 77
Scullcandy 160 72
Koss 95 67
Phillips/O’Neill 70 58
Denon 70 40
JVC 35 27

a. Does the t test indicate a significant relationship between price and the overall score?

The test t-Conclusion at α = .05

t =


(to 2 decimal places.)

p-value is



What is your conclusion? Use α = .05.



.

b. Test for a significant relationship using the F test.
p-value is



What is your conclusion? Use α = .05.

Because p-value is



.05, we



H0: β1 is



.

c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary.

Source of
Variation
Sum of
Squares
Degrees of
Freedom
Mean Square F p-value
Regression










Error





Total













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