الاحصاء الهندسي

ISE 325 Engineering Statistics Quiz Sample

  1. In a filling operation, the target fill volume is 120 ml. Inspectors have suspected that the mean fill volume has changed. The industrial engineer has decided to perform the statistical hypothesis testing:
    H0: μ = 120 ml
    H1: μ ≠ 120 ml
    He took a random sample of 8 observations and they are
    125 121
    119 127
    120 114
    126 121

    Test this hypothesis at level of significance 0.05, and state the conclusion of the test very clearly.

  2. Consider the hypothesis on the population variance:
    H0: σ2 = 0.5
    H1:σ2 > 0.5
    The acceptance region is selected by manufacturing to be [0, 0.78]. A random sample of 15 observations has been collected.
    1. Compute the probability of type I error.
    2. Compute the probability of type II error if the true variance is 0.8.
  3. In the Nestle Nescafe production line, the quality engineer has observed that the 200-g Nescafe jars coming out of the coffee filling machine do not confirm to the target weight of 200 g. He suspects that the filling machine deteriorates over time and it has to be recalibrated as it works for extended periods of time. To confirm his suspicion, he monitored the machine for different time durations and measured the weight of the filled jars, and he came up with the following numbers:
    Observation Weight (g)

    y

    		 Operation duration (hours)

    x
    1 192.96 4.1
    2 190.43 6.1
    3 180.19 9.5
    4 197.86 2.1
    5 196.35 3.6
    6 186.34 8.9
    7 194.02 3.2
    8 192 2.7
    9 183.08 7.6
    10 190.27 5.3

    He believes a linear regression model will be adequate to explain the variability in the weight of the filling.

    1. Estimate the values of b0, b1, s2, V(b0), and V(b1).
    2. Construct a 95% confidence interval on the slope of the regression line.

Dr Muhammad Al-Salamah