A manufacturer of metal plates makes two claims concerning the thickness of the plates they produce. The manufacturer claims that • Statement A: The mean is 200mm • Statement B: The variance is 1.5mm2 . To investigate Statement A, the thickness of a sample of metal
Question 2
A manufacturer of metal plates makes two claims concerning the
thickness of the plates they produce. The manufacturer claims that
• Statement A: The mean is 200mm
• Statement B: The variance is 1.5mm2
.
To investigate Statement A, the thickness of a sample of metal plates
produced in a given shift was measured. The values found are listed
in Part (a) of worksheet ‘Dataset2’, with millimetres (mm) as unit.
1. Calculate the sample mean and sample standard deviation for the
data in Part (a) of ’Dataset2’.
2. Set up the framework of an appropriate statistical test on Statement A. Explain how knowing the sample mean before carrying
out the test will influence the structure of your test.
3. Carry out the statistical test and state your conclusions.
To investigate the second claim, the thickness of a second sample of
metal sheets was measured. The values found are listed in Part (b) of
worksheet ‘Dataset2’, with millimetres (mm) as unit.
1. Calculate the sample mean and then the sample variance and
standard deviation for the data in Part (b).
2. Set up the framework of an appropriate statistical test on Statement B. Explain how knowing the sample variance before carrying out the test would influence the structure of your test.
Page 3
3. Carry out the statistical test and state your conclusions
| Part (a) | |||||
| 199.13 | 197.45 | 197.36 | 206.31 | 205.59 | 198.39 |
| 197.25 | 199.44 | 196.55 | 207.15 | 203.74 | 200.33 |
| 196.20 | 197.58 | 198.44 | 205.29 | 201.96 | 199.22 |
| 198.00 | 195.89 | 198.98 | 203.38 | 200.90 | 199.37 |
| 198.46 | 197.59 | 200.88 | 203.04 | 201.43 | 199.46 |
| 198.25 | 195.82 | 202.15 | 204.17 | 203.21 | 197.56 |
| 196.66 | 194.95 | 201.71 | 205.29 | 202.86 | 196.52 |
| Part (b) | |||||
| 194.95 | 196.13 | 202.70 | 203.37 | 201.25 | 198.44 |
| 196.27 | 195.64 | 204.50 | 203.61 | 200.04 | 199.18 |
| 197.13 | 203.70 | 204.37 | 202.25 | 199.44 | 197.27 |
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