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Math Help - Confidence interval,sample mean,Mode,standard deviation,Median

  1. #1
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    Confidence interval,sample mean,Mode,standard deviation,Median

    Can you tell me if my answers true,and How can i obtain the confidence interval?



    a)A samle of 10 students scored the following grades:

    40,42,35,54,57,54,46,42,54,57

    (i)Find the sample mean ,mode and median.

    Sample mean:








    Sample mode:

    mode is the most frequently ocurring value:

    grades frequency

    40 0

    42 2

    35 0

    54 3

    57 2

    46 0

    In this example we have more than one modal (multimodal)

    Mode=42,54,57



    Median:

    First we must arrange the numbers in increasing order.

    35,40,42,42,46,54,54,54,57,57

    Here the batch size is even,so we have 2 middle values:

    First middle value occure at the position(n/2)=(10/2=5)

    The first middle value is 46
    second middle value occure at the position[(n/2) +1]=6

    The second middle value is 54

    Median =[(46+54)/2]=50

    (ii)Compute the sample standard deviation





    (iii)Find 90%and 95%confidence intervals for the scores


    How can I get the confidence interval ..

    Here the sample size is <25 (sample size=10)

    I know how to obtain the confidence interval when the sample size >25

    buthow to obtain the confidence interval when the sample size <25

    (B)Suppose that the grades in a course are normally distributed with mean 69 and standard deviation 12.

    (i)Determine the ranges in which 90%,95%,and 99% of grades lie.

    Approximately 90%grades were between:

    ( -1.64 *σ) and (+1.64 *σ)

    (69-1.64*12) and(69+1.64*12)

    (69-19.68) and (69+19.68)

    49.32 and 88.68

    ================================
    Approximately 95%grades were between:
    ( -1.96*σ) and (+1.96*σ)
    (69-1.96*12) and(69+1.96*12)

    (69-23.52) and(69+23.52)

    45.48 and 92.52

    =================
    Approximately 95%grades were between:

    ( -2.58*σ) and (+2.58*σ)

    (69-2.58*12) and(69+2.58*12)

    (69-30.96) and(69+30.96)

    38.04 and 99.96

    ==============================

    (ii)Write down the mean and the standard error of the mean of samples of size 144.

    Since n>25

    x==69







    (iii)Find a range of values within which the means of approximately 95% of sample of size 144 lie.


    Last edited by change_for_better; May 27th 2009 at 09:25 PM.
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  2. #2
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    Quote Originally Posted by change_for_better View Post
    Can you tell me if my answers true,and How can i obtain the confidence interval?



    a)A samle of 10 students scored the following grades:

    40,42,35,54,57,54,46,42,54,57

    (i)Find the sample mean ,mode and median.

    [snip]

    In this example we have more than one modal (multimodal)

    Mode=42,54,57

    [snip]
    By definition the mode is 54. Why have you included 42 and 57?
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    By definition the mode is 54. Why have you included 42 and 57?

    Thank you for alerting me .. I think that we must include the numbers that occure more than once


    Can you help me in the following point


    (iii)Find 90%and 95%confidence intervals for the scores


    How can I get the confidence interval ..


    Here the sample size is <25 (sample size=10)

    I know how to obtain the confidence interval when the sample size >25

    buthow to obtain the confidence interval when the sample size <25
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  4. #4
    MHF Contributor matheagle's Avatar
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    IF you are using S, then you need normality and this would be a t distribution with n-1=9 degrees of freedom.
    So the 1.96 is incorrect.

    And the interval is \biggl(\bar X-t_{n-1,\alpha/2}{S\over \sqrt n} , \bar X+t_{n-1,\alpha/2}{S\over \sqrt n}\biggr)
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  5. #5
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    Quote Originally Posted by change_for_better View Post
    Thank you for alerting me .. I think that we must include the numbers that occure more than once Mr F says: No!

    Can you help me in the following point
    Read again carefully the definition you posted:

    mode is the most frequently ocurring value
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