A STATISTICS PROJECT

ASTATISTICSPROJECT

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Module2 Homework Assignment

  1. 459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.

Solution:

InstructorComments

  1. Find the critical values for that corresponds to the given confidence level of 98%.

Solution:

=2.326

InstructorComments:

  1. Find the critical value for corresponding to n = 12 and 95% confidence level.

Solution:

InstructorComments:

  1. Use the confidence level and sample data to find the margin of error E. College students’ annual earnings: 99% confidence, n = 74, = $3967, s = $874

Solution:

InstructorComments:

  1. Construct the confidence interval for question 4 above.

Solution:

InstructorComments:

  1. Write a statement that correctly interprets the confidence interval found in question 5.

Solution:

Weare 99% confident that the range from 3705 to 4229 entails the realvalue of μ. Thus, if we were to choose many diverse samples of thesame size and make the corresponding confidence intervals, in thelong run, 99% of them would contain the value of μ.

InstructorComments:

  1. Find the critical value corresponding to a sample size of 19 and a confidence level of 99%.

Solution:

N=19,degree of freedom = n-1 = 19-1 =18

CI=0.99

Theareas to the left of =

Fromthe Chi-square table, using Df = 18, the area 0.995

InstructorComments:

  1. Find the critical value corresponding to a sample size of 19 and a confidence level of 99%.

Solution:

N=19,degree of freedom = n-1 = 19-1 =18

CI=0.99

Theareas to the right of =

Fromthe Chi-square table, using Df = 18, the area 0.005

Thecritical value is

InstructorComments:

  1. The values listed below are the waiting times (in minutes) of customers at the Bank of Providence, where customers enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation and write a statement that correctly interprets the results.

4.25.4 5.8 6.26.77.7 8.59.310.0

4.2

-2.889

8.346

5.4

-1.689

2.853

5.8

-1.289

1.662

6.2

-0.889

0.790

6.7

-0.389

0.151

7.7

0.611

0.373

8.5

1.411

1.991

9.3

2.211

4.889

10.0

2.911

8.474

63.8

N=10,degree of freedom = n-1 = 9-1 =8

CI=0.95

Theareas to the right of =

Theareas to the left of =

Fromthe Chi-square table, using Df =8, the areas 0.025 and 0.975 thecritical values are:

Thecritical values are

Statement:with 95%confidentwe can say that thepopulation standard deviation is between 1.2975 and 3.6798.

InstructorComments:

  1. You want to estimate S for the population of waiting times at a fast-food restaurant’s drive-up windows, and you want to be 95% confident that the sample standard deviation is within 20% of S. Find the minimum sample size needed. Is this sample size practical?

Solution:

Accordingto Triola(2006) when having noprior knowledge of p ˆ, mathematicians dispense the specific valuesfor p ˆ = 0.5 and q ˆ= 0.5. The sample size obtained by making useof these values will be large enough to ensure the specified degreeof confidence. Hence,

References

Triola,M. F. (2006).&nbspElementarystatistics.Reading, MA: Pearson/Addison-Wesley.