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    Category :Math/Stat Homework

    Posted By:AccountingExpert

    Price Offered : $20

    Posting Date : 2014/06/12 11:13

    Due Date : 2014/06/25 12:00

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    MATH 1131 3.00 A S1
    Assignment 4
    Total marks = 60
    Question 1: Here are the weights (in kilograms) of a random sample of 24
    male runners
    67.8 61.9 63.0 53.1 62.3 59.7 55.4 58.9
    60.9 69.2 63.7 68.3 64.7 65.6 56.0 57.8
    66.0 62.9 53.6 65.0 55.8 60.4 69.3 61.7
    Suppose that the standard deviation of the population of weights is known
    to be σ = 4.5 kg.
    (a) (4 marks). Stating any additional assumptions, give a 95% condence
    interval for the population mean weight µ. Are you quite sure that µ
    is less than 65 kg? Why?
    (b) (3 marks). How many male runners would you have needed to estimate
    µ with a margin of error equal to 1 kg with 95% condence?
    (c) (2 marks). Based on the condence interval you gave in part (a), does
    a test of
    H0 : µ = 61.3 kg
    Ha : µ = 61.3 kg
    reject H0 at the 5% signicance level? Why?
    (d) (2 marks). Would H0 : µ = 65 be rejected at the 5% level if tested
    against a two-sided alternative? Why?
    Question 2: An agronomist examines the cellulose content of a variety of
    alfalfa hay. Suppose that the cellulose content in the population has standard
    deviation σ = 8 milligrams per gram (mg/g). A sample of 15 cuttings has
    mean cellulose content x = 145 mg/g.
    ¯

    1

    (a) (2 marks). Give a 90% condence interval for the population mean
    cellulose content µ.
    (b) (7 marks). A previous study claimed that the mean cellulose content
    was µ = 140 mg/g, but the agronomist believes that the mean is higher
    than that gure. State H0 and Ha and carry out a signicance test to
    see if the new data support this belief.
    (c) (2 marks). The statistical procedures used in (a) and (b) are valid
    when certain assumptions are satised. What are these assumptions?
    Question 3: You want to see if a redesign of the cover of a mail-order
    catalogue will increase the mean sales µ. A random sample of 900 customers
    are to receive the catalogue with the new cover. For planning purposes,
    you are willing to assume that the sales from the new catalogue will be
    approximately normally distributed with σ = 50 dollars. The mean sales for
    the original catalogue is 25 dollars. You wish to test
    H0 : µ = 25
    Ha : µ > 25
    You decide to reject H0 if the sample mean sales x > 26 and to accept H0
    ¯
    otherwise.
    (a) (2 marks). Find the probability of a Type I error, that is, the probability that your test rejects H0 when in fact µ = 25 dollars.
    (b) (2 marks). Find the probability of a Type II error when µ = 28 dollars.
    This is the probability that your test accepts H0 when in fact µ = 28.
    (c) (2 marks). Find the probability of a Type II error when µ = 30.
    (d) (2 marks). The distribution of sales is not normal because many customers buy nothing. Why is it nonetheless reasonable in this circum¯
    stance to assume that the sample mean sales X will be approximately
    normal?

    2

    Question 4: A company medical director failed to nd signicant evidence
    that the mean blood pressure of a population of executives diered from
    the national mean µ = 128. The medical director now wonders if the test
    used would detect an important dierence if one were present. For a random
    sample of size 72 from a normal population of executive blood pressures with
    standard deviation σ = 15, the z statistic is

    z = (¯ − 128)/(15/ 72)
    x
    The two-sided test rejects
    H0 : µ = 128
    at the 5% level of signicance when |z| ≥ 1.96.
    (a) (5 marks). Find the power of the test against the alternative µ = 135.
    (b) (4 marks). Find the power of the test against µ = 121. Can the test
    be relied on to detect a mean that diers from 128 by 7?
    (c) (1 mark). If the alternative were farther from H0 , say µ = 138, would
    the power be higher or lower than the values calculated in (a) and (b)?
    Question 5: (10 marks). Assume rents of one-bedroom apartments are
    normally distributed. A random sample of 10 one-bedroom apartments from
    your local newspaper has these monthly rents (in dollars):

    500

    650

    600

    505

    450

    550

    515

    495

    650

    395

    Do these data give reason to believe that the mean rent of all advertised
    apartments is greater than $500 per month? State hypotheses, nd the t
    statistic and its p-value, and state your conclusion.
    Question 6: (2 marks). Large trees growing near power lines can cause
    power failures during storms when their branches fall on the lines. Power
    companies spend a great deal of time and money trimming and removing
    trees to prevent this problem. Researchers are developing hormone and
    chemical treatments that will stunt or slow tree growth. If the treatment
    3

    is too severe, however, the tree will die. In one series of laboratory experiments on 216 sycamore trees, 41 trees died. Give a 95% condence interval
    for the proportion of sycamore trees that would be expected to die from this
    particular treatment.
    Question 7: (2 marks). A national opinion poll found that 44% of all American adults agree that parents should be given vouchers good for education
    at any public or private school of their choice. The result was based on a
    small sample. How large a random sample is required to obtain a margin of
    error of ±0.03 (i.e., ±3%) in a 95% condence interval? (use the previous
    poll’s result to obtain the guessed value p∗ .)
    Question 8: (6 marks). Of the 500 respondents in a Christmas tree telephone survey, 44% had no children at home and 56% had at least one child at
    home. The corresponding gures for the most recent census are 48% with no
    children and 52% with at least one child. Test the null hypothesis that the
    telephone survey technique has a probability of selecting a household with
    no children that is equal to the value obtained by the census. Give the z
    statistic and the p-value. What do you conclude?

    Answer
    Submitted by AccountingExpert on 2014/06/12 11:24
    teacher rated 211 times

    Price: $10.00

     

    A. Determine the order size for Company A in the given scenario that would minimize total annual cost by using the economic order quantity model, showing all of your work.






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    Answer
    Submitted by AccountingExpert on 2014/06/12 11:16
    teacher rated 211 times

    Price: $20.00

     

    Math1131 Assignment 4 100% Quality work A+ Guaranteed Tutorial Already Graded with A+ score




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