Statistical Analysis and Hypothesis Testing in Experimental Research and Population Studies

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Statistical Analysis and Hypothesis Testing in Experimental Research andPopulation Studies1.For a population with a standard deviation ofσ= 20, how large a sample is necessary tohave a standard error that is:a. less than or equal to 10 point?Letis the standard deviation of the population andis the size of the sample drawn.Letis the mean of the sample. Then the standard error of sample mean is defined as,.Here20 and10,MMnMnobtain the minimum required value of.2010101024 .Mnnnnnb. less than or equal to 4 points?Letis the standard deviation of the population andis the size of the sample drawn.Letis the mean of the sample. Then the standard error of sample mean is defined as,.Here20 and4,MMnMnobtain the minimum required value of.20444525 .Mnnnnnc. less than or equal to 2 point?Letis the standard deviation of the population andis the size of the sample drawn.Letis the mean of the sample. Then the standard error of sample mean is defined as,.Here20 and2,MMnMnobtain the minimum required value of.2022210100 .Mnnnnn2.The following samples were obtained from a population with a mean ofμ= 40 and astandard deviation ofσ= 8. Find the z-score corresponding to each sample mean.a. A sample of n = 4 scores with M = 38

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384020.5484MMMZn .b. A sample of n = 16 scores with M = 38384021.02816MMMZn .c. A sample of n = 64 scores with M = 38384022.01864MMMZn .3.Jumbo shrimp are those that require 10 to 15 shrimp to make a pound. Suppose that thenumber of jumbo shrimp in a 1-pound bag averagesμ= 12.5 with a standard deviation ofσ=1, and forms a normal distribution. What is the probability of randomly picking asample on n=25 1-pound bags that average more than M=13 shrimp per bag?Thescore when13 is,1312.50.52.50.2125The probability of randomly picking a sample on25 1-pound bags that average morethan13 shrimp per bag,2.512.512.510.9938MZMMMZnnMP ZP Z 0.0062 .4.A population forms a normal distribution with a mean ofμ= 75 and a standard deviationofσ= 20.a. What proportion of the sample means for n = 25 have values less than80? In otherwords, find P(M < 80) for n = 25.80755Thescore when80 and25 is,1.25 .42025MMMZMnZnThe proportion of the sample means for25 have values less than 80,1.251.250.8944 .nP Z b. What proportion of the sample means for n = 100 have values greater than 79? In otherwords, findP(M > 79) for n = 100.

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