SECTION 2. STATISTICAL ANALYSIS OF DATA

Answer ONE question from this Section.

3. Answer BOTH parts.

    1. Twenty independent assessments are made of the melting point - in degrees Centigrade - of a substance, with the following results:

      2. 22 23 22 22 25 20 24 25 24 20 26 23 26 22 22 20 25 21 22 22

      Find the minimum, maximum, mean and standard deviation for these melting point measurements. Then, stating any assumptions you may make, form a 90% confidence interval for the mean of the population.

    2. A manufacturer offers PTFE in pellet form and claims that two-thirds of the pellets will pass an opacity test. A random sample of m=5 pellets is taken from the large number in a carton and the numbe

    A random sample of 25 cartons from the manufacturer’s production is tested, with the following results for r:

    No. passing test, r

    0

    1

    2

    3

    4

    5

    Carton count

    1

    4

    7

    8

    3

    2

    Use these observed values to estimate the true proportion of produced pellets that would pass the test. Stating any assumptions you may make, test at a five-percent significance level the null hypothesis that the true proportion is two-

     

     

     

     

    The partition coefficient, KOW, of H2S from a particular crude oil to water is measured at six different temperatures, T deg C, with results as follows:

    x=T deg C

    0

    20

    40

    60

    80

    100

    y=KOW

    0.123

    0.176

    0.240

    0.314

    0.420

    0.517

    [For your assistance, å y2=0.3787, å xy=117.26]

    Find the least-squares straight-line regression of y on x, and calculate the residuals between this line and the six observed values for T. Why might a quadratic regression give a better fit to these data? Set out the equations you woul

    Construct a 90% confidence interval for your estimate of the slope of the straight line regression, stating any assumptions you may make in order to construct this interval.

    [For your assistance, the residual sum of squares about the line y=a+bx is given by S=å e2 =å y2-aå y-bå xy. Also Var(b)= s 2/[å x2 – (å x)2/n], where s 2 is the common variance for observations on y]