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14 January, 07:30

The customer service manager for the XYZ Fastener Manufacturing Company examined 60 vouchers and found 9 vouchers containing errors. Find a 98 percent confidence interval for the proportion of vouchers with errors.

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Answers (2)
  1. 14 January, 07:40
    0
    = (0.043, 0.257)

    Explanation:

    p = 9/60 = 0.15

    Z score for 98% confidence interval = Z0.01 = 2.33

    The Confidence interval = (p + Z0.01 * sqrt (p * (1 - p) / n))

    = (0.15 + 2.33 * sqrt (0.15 * (1 - 0.15) / 60))

    = (0.15 + 0.107)

    = (0.043, 0.257)
  2. 14 January, 07:53
    0
    The Confidence Interval (CI) is calculated as (0.043, 0.257).

    The steps and expanation is shown below.

    Explanation:

    The formula for a Confidence Interval (CI) for a population proportion is given as

    p + z*[Sqrt (p (1 - p)) / n]

    Or

    p - z*[Sqrt (p (1 - p)) / n],

    p is the sample proportion, n is the sample size, and z * is the appropriate value from the standard normal distribution for your desired confidence level. The following table shows values of z * for certain confidence levels.

    For the 98% Confidence Interval, z*-value = 2.33

    p = 9/60 = 0.15, confidence level z * = 2.33 (From the standard table)

    0.15 + 2.33[Sqrt (0.15 (1 - 0.15)) / 60]

    OR

    0.15 - 2.33[Sqrt (0.15 (1 - 0.15)) / 60]

    0.15 + 0.107 or 0.15 - 0.107

    Confidence Interval is

    (0.043, 0.257)
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