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1 February, 21:13

From a random sample of 68 businesses, it is found that the mean time that employees spend on personal issues each week is 5.8 hours with a standard deviation of 0.35 hours. What is the 95% confidence interval for the amount of time spent on personal issues?

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  1. 1 February, 22:09
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    Answer: (6.4005, 4.925)

    Step-by-step explanation: n = sample size = 68

    σ = population standard deviation = 0.35 hours

    x = sample mean = 5.8

    We are to construct a 95% confidence level for population mean.

    This is given below as

    Confidence interval = x ± Zα/2 * σ/√n

    Where Zα/2 = critical value for a 2 tailed with 5 percent level of significance (that's α=5%) = 1.96

    Note that level of significance + confidence level = 100, hence a 95% confidence level will give a 5% level of significance

    For the upper limit of the 95% confidence interval, we have that

    x + Zα/2 * σ/√n

    5.8 + 1.96 (0.38/√68)

    5.8 + 1.96 (0.046)

    5.8 + 0.0875

    = 6.4005

    For the lower limit of the 95% confidence interval, we have that

    x - Zα/2 * σ/√n

    5.8 - 1.96 (0.38/√68)

    5.8 - 1.96 (0.046)

    5.8 - 0.0875

    =4.925
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