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Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College

Point Estimate. an estimate of a population parameter given by a single number. Examples of Point Estimates. Examples of Point Estimates. is used as a point estimate for ? .. Examples of Point Estimates. is used as a point estimate for ? . s is used as a point estimate for ?.. Error of Estimate.

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Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College

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    1. Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Eight Part 1 (Sections 8.1 to 8.3) Estimation

    2. Point Estimate an estimate of a population parameter given by a single number

    5. Examples of Point Estimates is used as a point estimate for ? . s is used as a point estimate for ?.

    6. Error of Estimate the magnitude of the difference between the point estimate and the true parameter value

    7. The error of estimate using as a point estimate for ? is

    8. Confidence Level A confidence level, c, is a measure of the degree of assurance we have in our results. The value of c may be any number between zero and one. Typical values for c include 0.90, 0.95, and 0.99.

    9. Critical Value for a Confidence Level, c the value zc such that the area under the standard normal curve falling between zc and zc is equal to c.

    11. Find z0.90 such that 90% of the area under the normal curve lies between z-0.90 and z0.90. P(-z0.90 < z < z0.90 ) = 0.90

    15. Common Levels of Confidence and Their Corresponding Critical Values

    16. Confidence Interval for the Mean of Large Samples (n ? 30)

    22. Create a 95% confidence interval for the mean driving time between Philadelphia and Boston. Assume that the mean driving time of 64 trips was 6.4 hours with a standard deviation of 0.9 hours.

    23. = 6.4 hours s = 0.9 hours c = 95%, so zc = 1.96 n = 64

    26. 95% Confidence Interval: 6.4 .2205 < ? < 6.4 + .2205 6.1795 < ? < 6.6205 We are 95% sure that the true time is between 6.18 and 6.62 hours.

    27. What if it is impossible or impractical to use a large sample? Apply the Students t distribution.

    28. Students t Variable

    29. The shape of the t distribution depends only only the sample size, n, if the basic variable x has a normal distribution. When using the t distribution, we will assume that the x distribution is normal.

    30. Table 6 in Appendix II gives values of the variable t corresponding to the number of degrees of freedom (d.f.)

    31. Degrees of Freedom d.f. = n 1 where n = sample size

    32. The t Distribution has a Shape Similar to that of the the Normal Distribution

    33. Find the critical value tc for a 95% confidence interval if n = 8.

    35. The mean weight of eight fish caught in a local lake is 15.7 ounces with a standard deviation of 2.3 ounces. Construct a 90% confidence interval for the mean weight of the population of fish in the lake.

    36. Mean = 15.7 ounces Standard deviation = 2.3 ounces. n = 8, so d.f. = n 1 = 7 For c = 0.90, Table 6 in Appendix II gives t0.90 = 1.895.

    38. The 90% Confidence Interval: 14.16 < ? < 17.24 We are 90% sure that the true mean weight of the fish in the lake is between 14.16 and 17.24 ounces.

    39. Review of the Binomial Distribution Completely determined by the number of trials (n) and the probability of success (p) in a single trial. q = 1 p If np and nq are both > 5, the binomial distribution can be approximated by the normal distribution.

    40. A Point Estimate for p, the Population Proportion of Successes

    41. Point Estimate for q (Population Proportion of Failures)

    42. For a sample of 500 airplane departures, 370 departed on time. Use this information to estimate the probability that an airplane from the entire population departs on time.

    43. Error of Estimate for p hat as a Point Estimate for p

    48. Out of 500 departures, 370 departed on time. Find a 99% confidence interval.

    49. 99% confidence interval for the proportion of airplanes that depart on time: E = 0.0506 Confidence interval is:

    51. The point estimate and the confidence interval do not depend on the size of the population. The sample size, however, does affect the accuracy of the statistical estimate.

    52. Margin of Error The margin of error is the maximal error of estimate E for a confidence interval. Usually, a 95% confidence interval is assumed.

    53. Interpretation of Poll Results The proportion responding in a certain way is

    54. A 95% confidence interval for population proportion p is:

    55. Interpret the following poll results: A recent survey of 400 households indicated that 84% of the households surveyed preferred a new breakfast cereal to their previous brand. Chances are 19 out of 20 that if all households had been surveyed, the results would differ by no more than 3.5 percentage points in either direction.

    56. Chances are 19 out of 20 19/20 = 0.95 A 95% confidence interval is being used.

    57. ... 84% of the households surveyed preferred 84% represents the percentage of households who preferred the new cereal.

    58. ... the results would differ by no more than 3.5 percentage points in either direction. 3.5% represents the margin of error, E. The confidence interval is: 84% - 3.5% < p < 84% + 3.5% 80.5% < p < 87.5%

    59. The poll indicates ( with 95% confidence): between 80.5% and 87.5% of the population prefer the new cereal.

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