To determine Write an opinion on whether the given sample of workers used hand rubbing with alcohol or hand washing with soap. Explanation Calculation: It is given that the mean and standard deviation of bacterial count for health care workers who use hand rubbing are 35 per hand and 59, respectively. The mean and standard deviation of bacterial count for the people who use hand washing are 69 per hand and 106, respectively. A random sample of 50 health care workers is considered. The mean bacterial count per hand ( x ¯ ) is less than 30. Sampling distribution of x ¯ : When a random sample of size n is selected from a population that is normally distributed , then the sampling distribution of x ¯ is also normally distributed. Properties: The mean of sampling distribution is equal to the mean of the population. μ x ¯ = E ( x ) = μ . The standard deviation of the sampling distribution is equal to the ratio of the population standard deviation and square root of sample size . σ x ¯ = σ n . When the sample size ( n ) is large relative to the population size ( N ), then σ n must be multiplied by the finite correction factor ( N − n ) ( N − 1 ) . For most sampling situations, the correction factor is close to 1 and is ignored. The standard deviation σ x ¯ is sometimes referred to as the standard error of the mean. For hand rubbing : The mean is μ x ¯ = E ( x ¯ ) = μ . μ x ¯ = μ = 35 Thus, the value of μ x ¯ is 35. Substitute σ as 59 and n as 50 in the formula σ n . σ x ¯ = 59 50 = 59 7.0711 = 8.3438 Thus, the value of σ x ¯ is 8.344. Central limit theorem: The central limit theorem states that the sampling distribution of x ¯ with mean μ x ¯ = μ and a standard deviation σ x ¯ = σ n will be approximately normal, as the sample size is greater than or equal to 30

13th Edition

ISBN: 9780134080215

Author: James T. McClave, Terry T Sincich

Publisher: PEARSON

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Chapter 6.3, Problem 47ACA

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Write an opinion on whether the given sample of workers used hand rubbing with alcohol or hand washing with soap.

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Chapter 6.3, Problem 46ACI

Chapter 6.3, Problem 48ACA

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