Review Problems

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Review Problems

• Stat 701 Illustrations

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One-Sample Problem
A sample of 12 radon detectors of a certain type
was selected, and each was exposed to 100 pCi/L
of radon. The resulting readings were as
follows 105.6, 90.9, 91.2, 96.9, 96.5, 91.3,
100.1, 105.0, 99.6, 107.7, 103.3, 92.4
Problem To test that the population mean reading
is 100, and to construct a confidence interval
for this population mean. Summary n 12, Xbar
98.375, S 6.1095
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Two-Sample Problem

• The deterioration of many municipal pipeline
  networks across the country is a growing concern.
  One technology proposed for pipeline
  rehabilitation uses a flexible liner threaded
  through existing pipe. The following data
  represents the tensile strength (psi) of liner
  specimens for when a certain fusion process was
  used and when this process was not used.
• The study intended to show that using the fusion
  process increased the mean tensile strength.

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Data

• No Fusion 2748, 2700, 2655, 2822, 2511, 3149,
  3257, 3213, 3220, 2753

• Fused 3027, 3356, 3359, 3297, 3125, 2910, 2889,
  2902

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Summary of Statistics
Descriptive Statistics Variable N
Mean Median StDev SE Mean NoFusion
10 2902.8 2787.5 277.3
87.7 Fused 8 3108.1 3076.0
205.9 72.8
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Comparative BoxPlots
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Problems to Demonstrate

• Testing Equality of Population Means Using T-Test
• Confidence Interval for the Difference of
  Population Means
• Testing Equality of Population Variances
• Confidence Interval for the Ratio of Population
  Variances

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Testing Equality of Means(Equal Variances)
Two Sample T-Test and Confidence Interval Two
sample T for NoFusion vs Fused N
Mean StDev SE Mean NoFusion 10 2903
277 88 Fused 8 3108
206 73 95 CI for mu NoFusion - mu Fused
( -455, 45) T-Test mu NoFusion mu Fused (vs
lt) T -1.74 P 0.050 DF 16 Both use Pooled
StDev 249
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Testing Equality and CI of Means(Unequal
Variances)
Two Sample T-Test and Confidence Interval Two
sample T for NoFusion vs Fused N
Mean StDev SE Mean NoFusion 10 2903
277 88 Fused 8 3108
206 73 95 CI for mu NoFusion - mu Fused
( -448, 38) T-Test mu NoFusion mu Fused (vs
lt) T -1.80 P 0.046 DF 15