California Christian College Statistics Worksheet


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1. Timex Group receives components from a supplier, which it uses in its own production. The
components are delivered in batches of 2000. The supplier claims that there are only 1%
defective components on average from its production. However, production occasionally gets
out of control and a batch is produced with 10% defective components. The firm wishes to
intercept these low-quality batches, so a sample of size 50 is taken from each batch and tested.
If two or more defectives are found in the sample, then the batch is rejected.
a) Describe the two types of error the firm might make in assessing batches of
b) Calculate the probability of each type of error given the data above.
c) If, instead, samples of size 30 were taken and the batch rejected if one or more
rejects were found, how would the error probabilities be altered?
d) The firm can alter the two error probabilities by choice of sample size and rejection
criteria. How should it set the relative sizes of the error probabilities
i. if the product might affect consumer safety?
ii. if there are many competitive suppliers of components?
iii. if the costs of replacement under guarantee are high?
2. Answer true or false, with reasons if necessary.
(a) There is no way of reducing the probability of a Type I error without simultaneously
increasing the probability of a Type II error.
(b) The probability of a Type I error is associated with an area under the distribution of
x assuming the null hypothesis to be true.
(c) It is always desirable to minimize the probability of a Type I error.
(d) A larger sample, ceteris paribus, will increase the power of a test.
(e) The significance level is the probability of a Type II error.
(f) The confidence level is the probability of a Type II error
3. Given the following sample data:
Test the null hypothesis that the true mean is equal to 12, against a two-sided alternative
hypothesis. Draw the distribution of x under the null hypothesis and indicate the rejection
regions for this test.

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