curve to determine how far above or below a standard score of zero you’d have to go until you hit the start of the most extreme 5% of this distribution. In other words, how far above or below zero do you have to go until you hit the start of the least likely 5% of sample means that you’re likely to get when the null hypothesis is true. If we take our one sample mean and convert it to a standard score our knowledge of the normal now tells us that if this standard score is greater than or equal to +1.96 or if this standard score is less than or equal to we’ll –1.96 know that our sample mean falls among the 5% of sample means that you’re least likely to get when the null hypothesis is true. We would know that the odds are less than 5% that our 25 seventh graders (remember them) were members of a population of typical, average seventh graders. See Figure 3.5. The only left at this point is to convert our sample mean to a standard score. Figure 3.5 To convert a number to a standard score you take that number, subtract the mean of all the other numbers in the set, and then divide this deviation score by the standard deviation of all the scores in the set. A standard score is the deviation of one number from the mean divided by the average amount that numbers deviate from their mean. The equation to convert a raw score to a standard score was… X – ZX = -------- σ It’s the same thing to take a sample mean and convert it to a standard score. We need to take the number that we’re converting to a standard score (our sample mean of 135), divide it by the average of all the sample means in the set, and then divide this number by the standard deviation of all the sample mean in the set. The equation for the standard score we need here becomes… - Z = -------- σ Z represents the standard score for a particular sample mean. M is the sample mean that is being converted to a standard score. represents the mean of the population (or σ the average of all the sample means). represents the standard deviation of all the sample means.
curve to determine how far above or below a standard score of zero you’d have to go until you hit the start of the most extreme 5% of this distribution. In other words, how far above or below zero do you have to go until you hit the start of the least likely 5% of sample means that you’re likely to get when the null hypothesis is true. If we take our one sample mean and convert it to a standard score our knowledge of the normal now tells us that if this standard score is greater than or equal to +1.96 or if this standard score is less than or equal to –1.96 we’ll know that our sample mean falls among the 5% of sample means that you’re least likely to get when the null hypothesis is true. We would know that the odds are less than 5% that our 25 seventh graders (remember them) were members of a population of typical, average seventh graders. See Figure 3.5. The only left at this point is to convert our sample mean to a standard score. Figure 3.5 To convert a number to a standard score you take that number, subtract the mean of all the other numbers in the set, and then divide this deviation score by the standard deviation of all the scores in the set. A standard score is the deviation of one number from the mean divided by the average amount that numbers deviate from their mean. The equation to convert a raw score to a standard score was… X – ZX = -------- σ It’s the same thing to take a sample mean and convert it to a standard score. We need to take the number that we’re converting to a standard score (our sample mean of 135), divide it by the average of all the sample means in the set, and then divide this number by the standard deviation of all the sample mean in the set. The equation for the standard score we need here becomes… - Z = -------- σ Z represents the standard score for a particular sample mean. M is the sample mean that is being converted to a standard score. represents the mean of the population (or the average of all the sample means). σ represents the standard deviation of all the sample means.
Introduction%20to%20Statistical%20Inference%209-15-08.docx