z Scores If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: -2.00, -1.00, 0, 1.00, 2.00? Why?
Short Answer
Expert verified
A z-score equal to 2.00 will be preferred because it is a positive value, which depicts that the test score attained is 2 standard deviations greater than the mean score.
Step by step solution
01
Given information
Four z-scores corresponding to the test score obtained in a statistics test are given as -2.00, -1.00, 0, 1.00, and 2.00.
02
Z-score
Az-score gives an overall idea of how many standard deviations a given observation is above or below the mean value.
In the case of a sample, a z-score is obtained as:
Harmonic Mean The harmonic mean is often used as a measure of center for data sets consisting of rates of change, such as speeds. It is found by dividing the number of values n by the sum of the reciprocals of all values, expressed asn∑1x(No value can be zero.) The author drove 1163 miles to a conference in Orlando, Florida. For the trip to the conference, the author stopped overnight, and the mean speed from start to finish was 38 mi/h. For the return trip, the author stopped only for food and fuel, and the mean speed from start to finish was 56 mi/h. Find the harmonic mean of 38 mi/h and 56 mi/h to find the true “average” speed for the round trip.In Exercises 21–24, find the mean and median for each of the two samples, then comparethe two sets of results.Pulse Rates Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 “Body Data”in Appendix B). Does there appear to be a difference?Male: 86 72 64 72 72 54 66 56 80 72 64 64 96 58 66Female: 64 84 82 70 74 86 90 88 90 90 94 68 90 82 80Mean Absolute Deviation Use the same population of {9 cigarettes, 10 cigarettes, 20 cigarettes} from Exercise 45. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not centre about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?In Exercises 33–36, use the range rule of thumb to identify the limits separating values that are significantly low or significantly highFoot Lengths Based on Data Set 2 “Foot and Height” in Appendix B, adult males have foot lengths with a mean of 27.32 cm and a standard deviation of 1.29 cm. Is the adult male foot length of 30 cm significantly low or significantly high? Explain.:In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.Speed Dating In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Can the results be used to describe the variation among attractiveness ratings for the population of adult males?5 8 3 8 6 10 3 7 9 8 5 5 6 8 8 7 3 5 5 6 8 7 8 8 8 7
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The formula for calculating a z-score is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.
Z-values larger than 3 are certainly possible at n=361 for normally distributed data. Indeed, the largest-magnitude z-score should exceed 3 more than half the time. (If the data were drawn from a non-normal distribution, it can happen as low as n=11.)
Use the following format to find a z-score: z = X - μ / σ. This formula allows you to calculate a z-score for any data point in your sample. Remember, a z-score is a measure of how many standard deviations a data point is away from the mean. In the formula X represents the figure you want to examine.
The area under the normal distribution curve shows probability. To calculate the area under the curve, we calculate the z-score and construct a z-score table that describes the percentage of area to the left of the z-score to give a defined comparison.
To find the probability for the area greater than z, look up the Z-score and subtract it from 1 (this is the same process for finding a negative Z-score). To find the probability for a negative Z-score look up the positive version on this table and subtract it from 1.
1 Answer. Z = (x - mean)/standard deviation. Assuming that the underlying distribution is normal, we can construct a formula to calculate z-score from given percentile T%.
A z-score tells us the number of standard deviations a value is from the mean of a given distribution. negative z-scores indicate the value lies below the mean. positive z-scores indicate the value lies above the mean.
The formula for calculating the Z Test statistic is Z = (x̄ - µ) / (σ / √n). Here x̄ is the sample mean, µ is the population mean, σ is the population standard deviation, and n represents the sample size.
The original Z-score formula was as follows: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5. X1 = ratio of working capital to total assets. Measures liquid assets in relation to the size of the company.
Z-scores are measured in standard deviation units.
The closer your Z-score is to zero, the closer your value is to the mean. The further away your Z-score is from zero, the further away your value is from the mean. Typically, you will not see Z-scores that are more than 3 standard deviations from the mean.
A Z-score table shows the percentage of values (usually a decimal figure) to the left of a given Z-score on a standard normal distribution. For negative Z-scores, look up the positive version on this table, and subtract it from 1.
A z-score tells how many standard deviations someone is above or below the mean. A z-score of -1.4 indicates that someone is 1.4 standard deviations below the mean. Someone who is in that position would have done as well or better than 8% of the students who took the test.
Find Z Scores For A Data Set : Example Question #6
Explanation: A z score is unique to each value within a population. To find a z score, subtract the mean of a population from the particular value in question, then divide the result by the population's standard deviation.
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