Q4 (Hypothesis Tests)
A machine fills boxes with chocolates. The factory claims that each box is filled with 1000g of
chocolates and the standard deviation of the filling process is known to be 50g. Customers have been complaining that the chocolate boxes are lighter than usual this year. To investigate, a sample of 120 boxes is taken, giving a mean of 900g. Form an appropriate hypothesis test to see if the claim made by the customers is substantiated. Assume a significance level of 5%.
(a) State the Null and Alternate Hypotheses
(b) Should we use the Z or the T test statistic? Calculate this test statistic.
(c) Find the critical value of the test statistic at the 5% level of significance.
(d) State your conclusion to the hypothesis test.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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