A sample of 5 buttons is randomly selected and the following diameters are measured in inches. Give a point estimate for the population vari

Question

A sample of 5 buttons is randomly selected and the following diameters are measured in inches. Give a point estimate for the population variance. Round your answer to three decimal places. 1.04,1.00,1.13,1.08,1.11

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Caroline 2 months 2021-09-29T00:52:32+00:00 1 Answer 0 views 0

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    2021-09-29T00:53:41+00:00

    Answer:

     s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}

    But we need to calculate the mean with the following formula:

    \bar X = \frac{\sum_{i=1}^n X_I}{n}

    And replacing we got:

    \bar X = \frac{ 1.04+1.00+1.13+1.08+1.11}{5}= 1.072

    And for the sample variance we have:

     s^2 = \frac{(1.04-1.072)^2 +(1.00-1.072)^2 +(1.13-1.072)^2 +(1.08-1.072)^2 +(1.11-1.072)^2}{5-1}= 0.00277\ approx 0.003

    And thi is the best estimator for the population variance since is an unbiased estimator od the population variance \sigma^2

     E(s^2) = \sigma^2

    Step-by-step explanation:

    For this case we have the following data:

    1.04,1.00,1.13,1.08,1.11

    And in order to estimate the population variance we can use the sample variance formula:

     s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}

    But we need to calculate the mean with the following formula:

    \bar X = \frac{\sum_{i=1}^n X_I}{n}

    And replacing we got:

    \bar X = \frac{ 1.04+1.00+1.13+1.08+1.11}{5}= 1.072

    And for the sample variance we have:

     s^2 = \frac{(1.04-1.072)^2 +(1.00-1.072)^2 +(1.13-1.072)^2 +(1.08-1.072)^2 +(1.11-1.072)^2}{5-1}= 0.00277\ approx 0.003

    And thi is the best estimator for the population variance since is an unbiased estimator od the population variance \sigma^2

     E(s^2) = \sigma^2

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