Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
SlideShare a Scribd company logo

Z tests test statistic

•Download as PPTX, PDF•
•

This document discusses z-tests and provides examples of how to perform z-tests to test differences between population and sample means. It explains how to test: - Population or hypothesized mean vs sample mean - Two sample means when standard deviations are known - Two sample means when the population standard deviation is known It then provides three examples applying z-tests: testing if a sample mean is higher than a population mean, comparing two teaching methods, and comparing exam scores between traditional and technology-based teaching methods. The last example asks the reader to help verify the hypothesis at α=0.05 level of significance.

1 of 10
Z- TESTS Test Statistics
TESTING THE SIGNIFICANT DIFFERENCE BETWEEN  Population or hypothesized mean, that is Population mean vs Sample mean  Two sample means and two sample standard deviations are known, that is Sample mean1 vs Sample mean 2  Two sample means and population standard deviation is known, that is Sample mean 1 vs Sample mean 2
TESTING THE SIGNIFICANCE BETWEEN MEANS  “ n is large or when n ≥ 30 and σ is known”  Population mean vs Sample mean
TESTING THE SIGNIFICANCE OF DIFFERENCE BETWEEN MEANS  “n is large or when n ≥ 30 and σ is unknown”  Sample mean 1 vs Sample mean 2 and 2 sample standard deviations are known.
TESTING THE SIGNIFICANCE OF DIFFERENCE BETWEEN MEANS  “n is large or when n ≥ 30 and σ is known”  Sample mean 1 vs Sample mean 2 and population standard deviation is known.
EXAMPLE 1 The average score in the final examination in College Algebra at ABC College is known to be 80 with a standard deviation of 10. A random sample of 39 students was taken from this year’s batch and it was found that they have a mean score of 84. Test at 5% level of significance. a. Is this an indication that this year’s batch performed better in College Algebra than the previous batches? b. Is the mean score in College Algebra of this year’s batch different from 80?
EXAMPLE 2 The dean of ABC College wants to know which method is better in teaching Chemistry. He took a random sample of 40 students handled by only one teacher in lecture and laboratory, and found it to have a mean final grade of 83 with a standard deviation of 7. Fifty students from a group handled by two different teachers in lecture and laboratory were randomly taken and it was found that they have a mean final grade of 87 with a standard deviation of 10. Does this indicate that a two- teacher setup is better than a one-teacher setup? Test at α =0.01
EXAMPLE 3 A Statistics teacher wants to know if students exposed to the use of technology in the classroom got significantly higher scores in Statistics exam than those who are exposed to the traditional chalk and talk method. She took a sample of 30 students exposed to technology and recorded their Statistics exam scores: 95 88 81 98 81 80 83 80 91 80 75 83 88 85 81 85 83 86 89 88 90 89 88 85 87 86 66 85 65 95 She then took a sample of 40 students who were taught using the traditional method 88 78 81 87 91 90 83 84 66 81 80 74 73 71 66 60 78 78 65 60 71 85 89 79 80 83 75 73 80 71 65 71 89 81 75 60 82 80 90 83 Help the teacher verify the hypothesis at α = 0.05.
EXERCISE 1. A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be 2.05 years, with sample standard deviation 0.82 years. However, it is thought that the overall population mean age of coyotes is 1.75. Do the sample data indicated that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use 0.01 level of significance.
2.

More Related Content

Z tests test statistic

  • 2. TESTING THE SIGNIFICANT DIFFERENCE BETWEEN  Population or hypothesized mean, that is Population mean vs Sample mean  Two sample means and two sample standard deviations are known, that is Sample mean1 vs Sample mean 2  Two sample means and population standard deviation is known, that is Sample mean 1 vs Sample mean 2
  • 3. TESTING THE SIGNIFICANCE BETWEEN MEANS  “ n is large or when n ≥ 30 and σ is known”  Population mean vs Sample mean
  • 4. TESTING THE SIGNIFICANCE OF DIFFERENCE BETWEEN MEANS  “n is large or when n ≥ 30 and σ is unknown”  Sample mean 1 vs Sample mean 2 and 2 sample standard deviations are known.
  • 5. TESTING THE SIGNIFICANCE OF DIFFERENCE BETWEEN MEANS  “n is large or when n ≥ 30 and σ is known”  Sample mean 1 vs Sample mean 2 and population standard deviation is known.
  • 6. EXAMPLE 1 The average score in the final examination in College Algebra at ABC College is known to be 80 with a standard deviation of 10. A random sample of 39 students was taken from this year’s batch and it was found that they have a mean score of 84. Test at 5% level of significance. a. Is this an indication that this year’s batch performed better in College Algebra than the previous batches? b. Is the mean score in College Algebra of this year’s batch different from 80?
  • 7. EXAMPLE 2 The dean of ABC College wants to know which method is better in teaching Chemistry. He took a random sample of 40 students handled by only one teacher in lecture and laboratory, and found it to have a mean final grade of 83 with a standard deviation of 7. Fifty students from a group handled by two different teachers in lecture and laboratory were randomly taken and it was found that they have a mean final grade of 87 with a standard deviation of 10. Does this indicate that a two- teacher setup is better than a one-teacher setup? Test at α =0.01
  • 8. EXAMPLE 3 A Statistics teacher wants to know if students exposed to the use of technology in the classroom got significantly higher scores in Statistics exam than those who are exposed to the traditional chalk and talk method. She took a sample of 30 students exposed to technology and recorded their Statistics exam scores: 95 88 81 98 81 80 83 80 91 80 75 83 88 85 81 85 83 86 89 88 90 89 88 85 87 86 66 85 65 95 She then took a sample of 40 students who were taught using the traditional method 88 78 81 87 91 90 83 84 66 81 80 74 73 71 66 60 78 78 65 60 71 85 89 79 80 83 75 73 80 71 65 71 89 81 75 60 82 80 90 83 Help the teacher verify the hypothesis at α = 0.05.
  • 9. EXERCISE 1. A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be 2.05 years, with sample standard deviation 0.82 years. However, it is thought that the overall population mean age of coyotes is 1.75. Do the sample data indicated that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use 0.01 level of significance.
  • 10. 2.