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    homework help!




    any1 who can do as much of this as possible!??

    6.Assuming that the following sample of 12 numbers arise from a Normal
    distribution with mean  and standard deviation σ = 5.2, obtain 95%, 99%
    and 99.9% confidence intervals for .
    92.3 98.4 102.1 100.5 105.3 96.5
    96.2 105.3 92.7 107.1 96.9 89.2

    7. For the data in Q6, evaluate the probability or p-value for testing the null
    hypothesis H0 :  = 100 against the two-sided alternative hypothesis
    H1 :  = 100. What evidence do the CIs in Q6 and this p-value offer in
    support of H0?

    8.A researcher in Human Resources Management wants to determine the
    mean monthly salary of bank managers, and has a budget of 900 to
    conduct a survey and construct a confidence interval based on survey
    responses. The researcher knows that the population standard deviation of
    monthly salary σ is 1000, and allows 1.50 to cover the cost of contacting
    each respondent. If the error in estimating the mean is to be less than
    100 with a 95% level of confidence, show that the required sample size
    is within budget.
    Is the budget sufficient if the researcher wishes to work with a 99%
    level of confidence?
    What budget is required if the researcher wishes to retain a 95% level
    of confidence, but wishes to reduce the associated error to 50?

    9. An initial sample of size 25 from a Normal population with mean  and
    standard deviation σ = 10 gives
    X = 54.3. Show that the test-statistic for
    testing the null hypothesis H0 :  = 50 against the two-sided alternative
    hypothesis H1 :  = 50 leads to a p-value less than 0.05.
    A further sample of size 75 is then taken from the same population, and it
    is proposed to reconsider the same hypothesis using the combined sample
    of 100 values.
    What values of the mean of these 100 values will lead to p-value
    greater than 0.05 when testing H0 for the combined sample?
    Consider the further sample: determine the values of the sample
    mean in this further sample which will make the final p-value greater
    than 0.05, and find the probability of obtaining a sample mean for
    the further sample in this range.


    10. A sample of size n = 40 is taken from a N
    
    , 10
    2
    
    population, and the
    data analysed by a consultant who, without taking statistical advice, has
    decided to reject H0 :  = 10 if X < 8 or X > 12.
    What is the probability that this rule results in the consultant making
    a Type I error?
    Having taking some statistical advice, the consultant decides to change
    the rule to one where the null hypothesis will be rejected if X < 10−c
    or X > 10 + c. What value should c take to make the probability of
    a Type I error equal to 0.05?

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