Hypothesis Testing Exercises

Hypothesis Testing Exercises

Worked solutions to these questions can be found here: [ Q1], Q2 and Q3 and Q4

1. [math][L2][/math] Imagine that you are a member of a team of scientific advisors considering whether genetic modification of crops has any health consequences for the population at large. Having some knowledge of statistics, you set up the issue as one of hypothesis testing.

   1. What would your null and alternative hypotheses be?

   2. Explain the interpretation of a Type I error and a Type II error in this context.

   3. What sort of costs would arise as a consequence of each type of error?

   4. What sort of sample evidence would be needed to enable a statistical conclusion to be reached?

   5. If suitable sample evidence were available, what advice would you give about the strength of the evidence that would be required to reject your null hypothesis?

2. [math][L2][/math] Weekly wages in a particular industry are known to be normally distributed with a standard deviation of £2.10. An economist claims that the mean weekly income in the industry is £72.40. A random sample of 35 workers yields a mean income of £73.20.

   1. What null hypothesis would you specify?

   2. Without any further information, explain the justification for choosing

      1. a two tailed alternative hypothesis[math];[/math]

      2. an upper one tailed alternative hypothesis.

   3. Perform the tests for each of these alternative hypotheses in turn, using

      1. [math]p[/math] values {[math]p-val = 0.0244[/math] (for two tailed test) and [math]p-val=0.0122[/math] (for upper tailed test}

      2. classical hypothesis tests

      at a [math]5\%[/math] level of significance.

3. [math][L2][/math] This question is a version of Question 2.

   Weekly wages in a particular industry are known to be normally distributed, with an unknown variance. An economist claims that the mean weekly income in the industry is £72.40. A random sample of [math]15[/math] workers gives a sample mean of £73.20 and a sample standard deviation of £2.50. Redo part (3) of Question 2 with this new information. You will need to use EXCEL to compute the [math]p[/math] values required. {Do not reject [math]H_0[/math] for both, two-tailed and upper tailed test}

4. [math][L2][/math] A motoring organisation is examining the reliability of imported and domestically produced vans. Service histories for [math]500[/math] domestically made and [math]500[/math] imported vans were examined. Of these, [math]159[/math] domestically produced vans and [math]121[/math] imported vans had repairs for breakdowns. Test the hypothesis that the true proportion of breakdowns to be expected in the two populations of vans is [math]0.35[/math],

   1. using a lower one sided alternative hypothesis for domestically produced vans[math];[/math] {[math]t=-1.5002[/math], do not reject [math]H_0[/math]}

   2. using a two-sided alternative hypothesis for imported vans. {[math]t=-5.0632[/math], reject [math]H_0[/math]}