Question

A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 1.5 hours

Answers

  1. Answer:

    The Sample Size Need To be at least 114

    Step-by-step explanation:

    According to the Question,

    • Given, A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours.

    The Maximum Error(E) is given as 1.5 hours and the standard deviation(σ) is 6.2 hours.

    • Now, For 99% Confident the level of value α is 0.01.

    α/2 = 0.01/2 ⇒ 0.005

    • Thus, From The table, We get that the value of Z_{alpha/2} is 2.58.

    Hence, the sample size n can be found as

    n = {\frac{(Z_{alpha/2} * Standard Deviation)}{E}}²

    n = {2.58 × 6.2}² / 1.5²

    n = 113.72 .

    So, The Sample Size Need To be at least 114.

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