Results 1 to 6 of 6

Math Help - Null Hypothesis, Alternative hypothesis, Critical Region..

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    3

    Null Hypothesis, Alternative hypothesis, Critical Region..

    I have a test coming up and these questions were given to prepare for the test! Please help! Thank you!

    (a) A survey on 50 claims for a particular class of customers of a motor insurance company found out that the average cost for car damage is £700 with a standard deviation of 400. The insurance manager believes instead that the average cost is £80 bigger.

    (i) Does the sample data suggest that the manager is right? Test at a 5% significance level the hypothesis that the average cost is £780. Specify: null hypothesis, alternative hypothesis, critical region and comment on the result of the test.

    (b) For the same type of accidents, the number of claims per vehicle insured is known to follow a Poisson distribution with mean 0.03 per year. Using the normal approximation to the Poisson distribution, compute the probability that a group of 400 insured cars produces :

    (i) Less than 10 claims per year.

    (ii) More than 20 claims per year.

    (c) Assuming the cost per claim is 780 with standard deviation of 400, claims’ frequency and portfolio’s size are as specified above:

    (i) Compute the risk premium.

    (ii) Compute the value at risk at 99.5% level for the Insurer losses.
    Last edited by CaptainBlack; August 6th 2011 at 03:22 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Null Hypothesis, Alternative hypothesis, Critical Region..

    Quote Originally Posted by Samantha24 View Post
    I have a test coming up and these questions were given to prepare for the test! Please help! Thank you!

    (a) A survey on 50 claims for a particular class of customers of a motor insurance company found out that the average cost for car damage is £700 with a standard deviation of 400. The insurance manager believes instead that the average cost is £80 bigger.

    (i) Does the sample data suggest that the manager is right? Test at a 5% significance level the hypothesis that the average cost is £780. Specify: null hypothesis, alternative hypothesis, critical region and comment on the result of the test.

    (b) For the same type of accidents, the number of claims per vehicle insured is known to follow a Poisson distribution with mean 0.03 per year. Using the normal approximation to the Poisson distribution, compute the probability that a group of 400 insured cars produces :

    (i) Less than 10 claims per year.

    (ii) More than 20 claims per year.

    (c) Assuming the cost per claim is 780 with standard deviation of 400, claims’ frequency and portfolio’s size are as specified above:

    (i) Compute the risk premium.

    (ii) Compute the value at risk at 99.5% level for the Insurer losses.
    What have you tried? Where are you stuck? Have you asked whoever gave you these questions for solutions or answers?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2011
    Posts
    3

    Re: Null Hypothesis, Alternative hypothesis, Critical Region..

    For part (a) this is what I did;

    H0 : m <= 700
    H1 : m > 700

    From my test statistic I got 1.41. This is less than 1.96. So you don't reject null hypothesis. Also we can't conclude anything is statistically significant. Therefore, we can't tell if the manger is right or not.

    For (b) I don't get what it means by Normal Approximation to the Poisson Distribution but this is what I did. Also I don't know if I should use the 5% significance level from before (If I did I could use the Poisson Table?).

    (i)

    P(X < 10) = P(0) + P(1) + .. + P(9)

    To calculate each value I use: P(X)= (e^-m)*(m^x)/ x!

    I don't know if I should be doing it like that or using the poisson table.. It doesn't seem to justify 4 marks..

    (ii)

    P(X > 20) = 1 - P(X < 20)

    From here I use the same method as before but have many more values..? I'm sure there must be a short cut as for 4 marks each.. Seems like a lot of work.

    Furthermore, what do I do with the 400? Does it just change my notation on my probabilities? I.e. P(X < 10, 400)?

    For part (c)

    (i)

    RP = average cost per claim * probability of claims. So RP= 780*[the answer I get from (b)(ii)]

    However, I don't know if my method of calculating in part (b)(ii) is correct, let alone (b)(i)..

    Finally,

    (ii) I'm completely lost..
    Last edited by Samantha24; August 7th 2011 at 08:57 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Null Hypothesis, Alternative hypothesis, Critical Region..

    Quote Originally Posted by Samantha24 View Post
    For part (a) this is what I did;

    H0 : m <= 700
    H1 : m > 700
    You are told what to use for the null-hypothesis in the question!

    for a one tailed test:
    H0 : m = 780
    H1 : m < 780

    for a two tailed test:
    H0 : m = 780
    H1 : m != 780

    CB
    Last edited by CaptainBlack; August 8th 2011 at 10:49 PM. Reason: correct typos (duplicated due to cut and paste :( )
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2011
    Posts
    3

    Re: Null Hypothesis, Alternative hypothesis, Critical Region..

    How do I know it's either one tailed or two tailed.. Do I show both one tailed and two tailed testing? Also I was thinking maybe it should be;

    H0 : m = 780
    H1 : m = 700

    or

    H0 :m = 780
    H1 :m != 780

    Does it matter how I phrase the hypotheesis testing? As I could phrase it in different ways?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Null Hypothesis, Alternative hypothesis, Critical Region..

    Quote Originally Posted by Samantha24 View Post
    How do I know it's either one tailed or two tailed.. Do I show both one tailed and two tailed testing? Also I was thinking maybe it should be;

    H0 : m = 780
    H1 : m = 700

    or

    H0 :m = 780
    H1 :m != 780

    Does it matter how I phrase the hypotheesis testing? As I could phrase it in different ways?
    First is wrong, the second is right (a typos in my earlier post, now corrected).

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: January 17th 2012, 07:37 AM
  2. Determining a null and alternative hypothesis
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: December 7th 2009, 07:47 AM
  3. hypothesis/critical region help
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 8th 2008, 05:30 PM
  4. Hypothesis testing critical region help
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: May 5th 2008, 06:02 AM
  5. Replies: 1
    Last Post: February 6th 2008, 02:27 PM

Search Tags


/mathhelpforum @mathhelpforum