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16 June, 13:48

In order to test whether the average waiting time this year differs from last year, a sample of 25 data were collected this year with a mean of 0.74 hours and standard deviation 0.22 hours. Calculate the 99% confidence interval for the true waiting time for banking service this year.

a. 0.74 ± 2.57 x 0.22/√25

b. 0.74 ± 2.797 x 0.22/√25

c. 0.74 ± 2.797 x 0.22/√24

d. 0.74 ± 2.787 x 0.22/√25

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Answers (2)
  1. 16 June, 14:00
    0
    a. 0.74 ± 2.57 x 0.22/√25

    Step-by-step explanation:

    Confidence interval is a range of values in which there is a specified probability that the value of a parameter lies within that range.

    The confidence interval of a statistical data can be written as.

    x+/-zr/√n ... 1

    Given;

    Mean gain x = 0.74 hours

    Standard deviation r = 0.22

    Number of samples n = 25

    Confidence interval = 99%

    z (at 99% confidence) = 2.57 (from the table)

    Substituting the values we have into equation 1;

    0.74+ / - 2.57*0.22/√25
  2. 16 June, 16:02
    0
    (B) 0.74 + or - 2.797 * 0.22/√25

    Step-by-step explanation:

    Confidence Interval = mean + or - t * sd/√n

    mean = 0.74 hours

    sd = 0.22 hours

    n = 25

    degree of freedom = n - 1 = 25 - 1 = 24

    Confidence level = 99%

    t-value corresponding to 24 degrees of freedom and 99% confidence level is 2.797

    Confidence Interval = 0.74 + or - 2.797 * 0.22/√25
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