A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled fi

Question

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

Today Five Years Ago
x 82 88
σ2 112.5 54
n 45 36

The standard deviation of the difference between the means of the two populations is ______.

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Eva 1 week 2021-09-15T14:13:42+00:00 1 Answer 0

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    2021-09-15T14:15:30+00:00

    Answer:The standard deviation of the difference between the means of the two populations is 2.

    Step-by-step explanation:

    The given table :

         Today  Five years ago

    \overline{x}=\ \ \ \  82\ \ \ \ \ 88\\\sigma^2=\ \ 112.5\ \ 54\\n=\ \ \ \ 45\ \ \ \ \ 36

    Let A denotes the scores from students enrolled today and B denotes the scores from students enrolled five years ago.

    Then, the standard deviation of the difference between the means of the two populations would be :-

    S.E._{\overline{x}_A-\overline{x}_B}}=\sqrt{\dfrac{\sigma^2_A}{n_1}+\dfrac{\sigma^2_B}{n_2}}\\\\=\sqrt{\dfrac{112.5}{45}+\dfrac{54}{36}}\\\\=\sqrt{4}=2

    Hence, the standard deviation of the difference between the means of the two populations is 2.

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45:7+7-4:2-5:5*4+35:2 =? ( )