Page 1 of 2 12 LastLast
Results 1 to 15 of 16

Math Help - Samplesof two types of electric components ....State the null hypothesis

  1. #1
    Banned
    Joined
    Dec 2008
    From
    Mauritius
    Posts
    523

    Samplesof two types of electric components ....State the null hypothesis

    Question :

    Samples of two types of electric component were tested for length of life and following data were determined:


    <br />
  **\qquad \qquad \qquad \qquad Type1 \qquad \qquad\qquad \qquad Type 2

    Sample \ size \qquad \qquad n_1 = 8 \qquad \qquad \qquad \qquad n_2 = 7

     Sample \ mean \qquad \quad \bar{x_1} = 1234 hrs \qquad \qquad \quad     \bar{x_2} = 1036 hrs

    <br />
Sample \ SD's \qquad \quad S_1 = 36  hrs \qquad \qquad \qquad  S_2 = 40 hrs <br />


    Is the difference in means sufficient to say that Type 1 is superior to Type 2 regarding length of life ? State the null hypothesis.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zorro View Post
    Question :

    Samples of two types of electric component were tested for length of life and following data were determined:


    <br />
  **\qquad \qquad \qquad \qquad Type1 \qquad \qquad\qquad \qquad Type 2

    Sample \ size \qquad \qquad n_1 = 8 \qquad \qquad \qquad \qquad n_2 = 7

     Sample \ mean \qquad \quad \bar{x_1} = 1234 hrs \qquad \qquad \quad     \bar{x_2} = 1036 hrs

    <br />
Sample \ SD's \qquad \quad S_1 = 36  hrs \qquad \qquad \qquad  S_2 = 40 hrs <br />


    Is the difference in means sufficient to say that Type 1 is superior to Type 2 regarding length of life ? State the null hypothesis.
    The null htpotheseis is that the means are equal, now what test do you use for sample means from small samples with standard deviation estimated from the samples?

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Dec 2008
    From
    Mauritius
    Posts
    523

    Is this correct?

    Quote Originally Posted by CaptainBlack View Post
    The null htpotheseis is that the means are equal, now what test do you use for sample means from small samples with standard deviation estimated from the samples?

    CB
    This is my work please take a look and tell me if i have done any thing wrong

    H_0 : \mu - \mu = 0
    H_a : \mu - \mu > 0
    \alpha : 0.05

    Is this correct ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zorro View Post
    This is my work please take a look and tell me if i have done any thing wrong

    H_0 : \mu - \mu = 0
    H_a : \mu - \mu > 0
    \alpha : 0.05

    Is this correct ?
    It looks like you are supposed to use a two sample unpaired t-test (because the sample sizes are small) with unequal sample sizes (see Student's t-test - Wikipedia, the free encyclopedia)

    The problem with this is that this requires that the distribution of component lives is normal, which is not usually the case and not given in the question.

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    Dec 2008
    From
    Mauritius
    Posts
    523

    Do u mean this test

    Quote Originally Posted by CaptainBlack View Post
    The null htpotheseis is that the means are equal, now what test do you use for sample means from small samples with standard deviation estimated from the samples?

    CB
    Do u mean this test

    t = \frac{\bar x_1 - \bar x_2 - k}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

    where s_p =  \frac{(n_1 -1)s_1 ^2 + (n_2 -1)s_2 ^2}{n_1 + n_2 - 2}

    but what should be the null hypothesis
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zorro View Post
    Do u mean this test

    t = \frac{\bar x_1 - \bar x_2 - k}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

    where s_p =  \frac{(n_1 -1)s_1 ^2 + (n_2 -1)s_2 ^2}{n_1 + n_2 - 2}

    but what should be the null hypothesis
    The null hypothesis is that the means are equal (and so in your notation that k=0)

    CB
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Banned
    Joined
    Dec 2008
    From
    Mauritius
    Posts
    523

    Is this correct?

    Quote Originally Posted by CaptainBlack View Post
    The null hypothesis is that the means are equal (and so in your notation that k=0)

    CB


    H_0 : \mu_1 - \mu_2 = 0
    H_a : \mu_1 - \mu_2 \ge 0
    \alpha : 0.05

    Is this correct ?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zorro View Post
    H_0 : \mu_1 - \mu_2 = 0
    H_a : \mu_1 - \mu_2 \ge 0
    \alpha : 0.05

    Is this correct ?
    Yes, for a one sided test ( H_a is that \mu_1 > \mu_2, note > not \ge as this includes the null-hypothesis) the two sided test would have H_a: |\mu_1-\mu_2| > 0

    CB
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    From the sample st deviations, I guess we can assume that the population variances are equal.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Banned
    Joined
    Dec 2008
    From
    Mauritius
    Posts
    523

    Is this correct please advice

    Quote Originally Posted by CaptainBlack View Post
    Yes, for a one sided test ( H_a is that \mu_1 > \mu_2, note > not \ge as this includes the null-hypothesis) the two sided test would have H_a: |\mu_1-\mu_2| > 0

    CB
    H_0 : \mu_1 - \mu_2 = 0
    H_a : | \mu_1 - \mu_2 | > 0
    \alpha = 0.05


    - Reject the null hypothesis if t > t_{\alpha,n_1 + n_2 -2} ie t > 1.771


    t = \frac{ \bar x_1 - \bar x_2 - 0}{S_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}
    where

    S_p = \frac{(n_1 - 1) s_1 ^2 + (n_2 - 1) s_2 ^2}{n_1 + n_2 -2}

    S_p = 1436

    Substituting S_p in the equation weget

    t = 0.26 < 1.771

    |t| < 1.771 therefore null hypothesis cannot be rejected

    Is this correct ?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by matheagle View Post
    From the sample st deviations, I guess we can assume that the population variances are equal.
    There is no reason to assume the variances are equal other than the near coincidence in numerical values. Given the high variability in sample variance (with such small sample sizes) I would stick to treating the variances as unequal.

    CB
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zorro View Post
    H_0 : \mu_1 - \mu_2 = 0
    H_a : | \mu_1 - \mu_2 | > 0
    \alpha = 0.05


    - Reject the null hypothesis if t > t_{\alpha,n_1 + n_2 -2} ie t > 1.771


    t = \frac{ \bar x_1 - \bar x_2 - 0}{S_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}
    where

    S_p = \frac{(n_1 - 1) s_1 ^2 + (n_2 - 1) s_2 ^2}{n_1 + n_2 -2}

    S_p = 1436

    Substituting S_p in the equation weget

    t = 0.26 < 1.771

    |t| < 1.771 therefore null hypothesis cannot be rejected

    Is this correct ?
    There is an error in the equation for pooled standard deviation, looks like you have used the pooled variance.

    CB
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    You can use an F test to determine if the population variances are equal.
    If you decide they are, then the test stat for the means is

    {\bar x_1- \bar x_2\over s_p\sqrt{ {1\over n_1}+{1\over n_2}}}

    otherwise you should use Satterthwaite's approximation

    {\bar x_1- \bar x_2\over \sqrt{ {s_1^2\over n_1}+{s_2^2\over n_2}}}

    http://www.unm.edu/~marcusj/PSE.pdf
    which has a typo in it, they squares the pooled sample variance incorrectly in line 11
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Banned
    Joined
    Dec 2008
    From
    Mauritius
    Posts
    523

    please provide the correct solution

    Quote Originally Posted by CaptainBlack View Post
    There is an error in the equation for pooled standard deviation, looks like you have used the pooled variance.

    CB
    Could u please provide me with the right solution. If the formula which i have not used is right then which one should i use

    In the prev post i asked u if the formula which i used was correct or no , at that time u didnt pointed out this error.....

    please let me know what is the right formula and also why , so that i dont make the same mistake again .
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zorro View Post
    Could u please provide me with the right solution. If the formula which i have not used is right then which one should i use

    In the prev post i asked u if the formula which i used was correct or no , at that time u didnt pointed out this error.....

    please let me know what is the right formula and also why , so that i dont make the same mistake again .
    What your formula gives is S_p^2 not S_p, so just take the square root of what you have.

    CB
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. state the null and alternative hypothsis
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: August 9th 2011, 08:38 PM
  2. Null Hypothesis, Alternative hypothesis, Critical Region..
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: August 8th 2011, 11:46 PM
  3. null hypothesis help
    Posted in the Statistics Forum
    Replies: 1
    Last Post: June 24th 2010, 06:09 PM
  4. Null Hypothesis
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 29th 2009, 02:24 PM
  5. calculate electric field components, simple
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: November 22nd 2008, 06:44 AM

Search Tags


/mathhelpforum @mathhelpforum