14. Claim: ₁2; α = 0.03 Population statistics: a₁ = 136 and ₂ = 215 Sample statistics: x₁=5004, n₁ = 144 and ₂ = 4895, n₂ 4895, n₂ = 156
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In Exercises 11 –14, test the claim about the difference between two population means u1 and u2 at the level of significance a. Assume the samples are random and independent, and the populations are
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- The number of contaminating particles on a silicon waferprior to a certain rinsing process was determined for eachwafer in a sample of size 100, resulting in the followingfrequencies:Number of particles 0 1 2 3 4 5 6 7Frequency 1 2 3 12 11 15 18 10Number of particles 8 9 10 11 12 13 14Frequency 12 4 5 3 1 2 1a. What proportion of the sampled wafers had at leastone particle? At least five particles?b. What proportion of the sampled wafers had betweenfive and ten particles, inclusive? Strictly between fiveand ten particles?c. Draw a histogram using relative frequency on thevertical axis. How would you describe the shape of thehistogram?Suppose that a random sample of size 1 is to be taken from a finite population of size N. a. How many possible samples are there?b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration.c. What is the difference between taking a random sample of size 1 from a population and selecting a member at random from the population?