A random sample of 100 workers in one large plant took an average of 12 minutes to complete a task, with a standard deviation of 2 minutes.

Question

A random sample of 100 workers in one large plant took an average of 12 minutes to complete a task, with a standard deviation of 2 minutes. A random sample of 50 workers in a second large plant took an average of 11 minutes to complete the task, with a standard deviation of 3 minutes. Construct a 95% confidence interval for the difference between the two population mean completion times.

in progress 0
Diễm Thu 3 years 2021-08-03T20:07:00+00:00 1 Answers 37 views 0

Answers ( )

  1. Sigrid
    0
    2021-08-03T20:08:08+00:00
    Reply

    Answer:

    The 95% Confidence Interval for the difference between the two population mean completion times =

    (0.081, 1.919)

    Step-by-step explanation:

    Confidence Interval for difference between two means =

    μ1 -μ2 ± z × √ σ²1/n1 + σ²2/n2

    Where

    μ1 = mean 1 = 12 mins

    σ1 = Standard deviation 1 = 2 mins

    n1 = 100

    μ2= mean 2 = 11 mins

    σ2 = Standard deviation 2 = 3 mins

    n1 = 50

    z score for 95% confidence interval = 1.96

    μ1 -μ2 ± z × √ σ²1/n1 + σ²2/n2

    = 12 – 11 ± 1.96 × √2²/100 + 3²/50

    = 1 ± 1.96 × √4/100 + 9/50

    = 1 ± 1.96 × √0.04 + 0.18

    = 1 ± 1.96 × √0.22

    = 1 ± 1.96 × 0.469041576

    = 1 ± 0.9193214889

    Confidence Interval

    = 1 – 0.9193214889

    = 0.0806785111

    ≈ 0.081

    1 + 0.9193214889

    = 1.9193214889

    ≈ 1.919

    Therefore, the 95% Confidence Interval for the difference between the two population mean completion times =

    (0.081, 1.919)

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )