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Statistical Analysis and Hypothesis Testing in Experimental Research and Population Studies

An assignment on statistical analysis and hypothesis testing in experimental and demographic studies.

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    Statistical Analysis and Hypothesis Testing in Experimental Research and Population Studies 1. For a population with a standard deviation of σ = 20, how large a sample is necessary to have a standard error that is: a. less than or equal to 10 point? Let is the standard deviation of the population and is the size of the sample drawn. Let is the mean of the sample. Then the standard error of sample mean is defined as, . Here 20 and 10, M M n M n         obtain the minimum required value of . 20 10 10 10 2 4 . M n n n n n            b. less than or equal to 4 points? Let is the standard deviation of the population and is the size of the sample drawn. Let is the mean of the sample. Then the standard error of sample mean is defined as, . Here 20 and 4, M M n M n         obtain the minimum required value of . 20 4 4 4 5 25 . M n n n n n            c. less than or equal to 2 point? Let is the standard deviation of the population and is the size of the sample drawn. Let is the mean of the sample. Then the standard error of sample mean is defined as, . Here 20 and 2, M M n M n         obtain the minimum required value of . 20 2 2 2 10 100 . M n n n n n            2. The following samples were obtained from a population with a mean of μ = 40 and a standard deviation of σ = 8. Find the z - score corresponding to each sample mean. a. A sample of n = 4 scores with M = 38

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    38 40 2 0.5 4 8 4 M M M Z n               . b. A sample of n = 16 scores with M = 38 38 40 2 1.0 2 8 16 M M M Z n               . c. A sample of n = 64 scores with M = 38 38 40 2 2.0 1 8 64 M M M Z n               . 3. Jumbo shrimp are those that require 10 to 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1 - pound bag averages μ = 12.5 with a standard deviation of σ =1, and forms a normal distribution. What is the probability of randomly picking a sample on n=25 1 - pound bags that average more than M=13 shrimp per bag?       The score when 13 is, 13 12.5 0.5 2.5 0.2 1 25 The probability of randomly picking a sample on 25 1-pound bags that average more than 13 shrimp per bag, 2.5 1 2.5 1 2.5 1 0.9938 M Z M M M Z n n M P Z P Z                          0.0062 . 4. A population forms a normal distribution with a mean of μ = 75 and a standard deviation of σ = 20. a. What proportion of the sample means for n = 25 have values less than 80? In other words, find P (M < 80) for n = 25. 80 75 5 The score when 80 and 25 is, 1.25 . 4 20 25 M M M Z M n Z n                   The proportion of the sample means for 25 have values less than 80, 1.25 1.25 0.8944 . n P Z      b. What proportion of the sample means for n = 100 have values greater than 79? In other words, find P (M > 79) for n = 100.

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