1. PROBABILITY AND STATISTICS
WEEK 10
Onur Doğan

2. Confidence Intervals
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3. Confidence Interval on the Mean of a Normal Distribution, Variance Known
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4. Confidence Interval Formula
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5. Example
Suppose that the life length of a light bulb follows the normal distribution. A random sample of n = 30 bulbs is tested and the sample mean is found to be 780 hours (s2 =402).
Construct a 95% two sided confidence interval on the mean life length (µ) of a light bulb.
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6. Example
The diameter of a hole (X; unit: in.) for a cable harness is normal with σ2= A random sample of n = 10 yields an average diameter of 1,5045 in.
Construct a 99% upper-confidence bound on the mean diameter (p) of the hole.
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7. Confidence Interval on the Mean of a Normal Distribution,Variance Unknown (t distribution)
Small Sample CI?
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8. Example
You sample 36 apples from your farm’s harvest of over apples. The mean weight of the sample is 112 grams (with a 40 gram sample standart deviation). What is the probability that the mean weight of all apples is within 100 and 124 grams?
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9. A Large-Sample Confidence Interval for a Population Proportion
Confidence Interval Formula:
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10. Example
A sample of n = 40 bridges in a city is tested for metal corrosion, and x = 28 bridges are found corroded.
Construct a 95% two-sided confidence interval on the proportion of corroded bridges (p) in the county.
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11. Example
In a teaching district school management allows teacher using computer in their lessons. From the 6000 teachers in district, 250 were randomly selected and asked if they felt that computers were an essential teaching tool for their classroom. Of those selected, 142 teachers felt that computers were an essential teaching tool.
Calculate a 99% confidence interal for the proportion of teachers who felt that computers are an essential teaching tool
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12. Summary for Confidence Intervals
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13. Hypothesis Testing
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14. Test Regions
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15. Test Errors
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16. Hypothesis Testing Procedure
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17. Tests on the Mean of a Normal Distribution, Variance Known.
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18. Example
For several years, a teacher has recorded his students' grades, and the mean, µ for all these students' grades is 72 and the standard deviation is σ = 12. The current class of 36 students has an average x = 75,2 (higher than µ = 72) and the teacher claims that this class is superior to his previous ones. Test the teacher’s claim for the level of significance = α=0,05.
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19. Relationship Between Hypothesis Test, CI and p-value
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20. Tests on a Population Proportion.
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21. Example
For the bridge example; a specialist claims that more than half of the bridges gave been corroded in the city. Test the specialist’s claim with %95 confidence.
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22. Example
Suppose that a factory is producing wheels for airbuses. The manufacturer claims that they produce wheels 3 meters diameter.
The quality control department of the buyer firm investigate a sample from the daily product. They controlled 36 wheels and found that average diamater is 2,92 and s.d. is 0,18.
Test the claim at α=0.05 significance level
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23. Example
According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the claim that the actual percentage is 53%. Use a 0.10 significance level.
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24. Example
The national weather service says that the mean daily high temperature for July in İzmir is 42°C. A local weather service wants to test the claim of 42°C because it believes it is different. A sample of mean daily high temperatures for October over the past 31 years yields =44°F and s=3.8°C. Test the claim at α=0.01 significance level.
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25. Example
In a clinical study of an allergy drug, 108 of the 203 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief.
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