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A one sample Z-test is used for hypothesis testing to compare a sample mean with a population mean to determine if the sample is representative of the population.
A one sample Z-test is used for hypothesis testing to compare a sample mean with a population mean to determine if the sample is representative of the population.
To conduct a one sample z-test, a researcher needs a random sample of a normally distributed, defined population (the population mean, and standard deviation must be identified).
To conduct a one sample z-test, a researcher needs a random sample of a normally distributed, defined population (the population mean, and standard deviation must be identified).
Follow These Easy Steps:
Follow These Easy Steps:
1. State the null and research hypothesis
1. State the null and research hypothesis
2. Set the level of significance
2. Set the level of significance
3. Compute the test statistic value (obtained value)
3. Compute the test statistic value (obtained value)
4. Determine the critical value to use for the rejection of the null hypothesis
4. Determine the critical value to use for the rejection of the null hypothesis
5. Compare the obtained value and the critical value
5. Compare the obtained value and the critical value
6. Decide if you will accept or reject the null hypothesis and if more research steps are needed
6. Decide if you will accept or reject the null hypothesis and if more research steps are needed
Suppose a teacher has decided to see if rewarding (bribing) students with candy to complete their daily homework will improve their performance on her end of the year assessments. After spending the year rewarding her students with sweet treats for their efforts, her class earned the following scores on the test:
Suppose a teacher has decided to see if rewarding (bribing) students with candy to complete their daily homework will improve their performance on her end of the year assessments. After spending the year rewarding her students with sweet treats for their efforts, her class earned the following scores on the test:
The sample mean is 87.53 for her current class of 30 students. Her records show that the mean of the assessment scores for her students over the past five years is 86.23 with a standard deviation of 7.5.
The sample mean is 87.53 for her current class of 30 students. Her records show that the mean of the assessment scores for her students over the past five years is 86.23 with a standard deviation of 7.5.
Watch the videos below to see how we can use a Z-Test to determine if the sample scores are different from the population score collected using the same assessment:
From the calculations presented in the videos, there is not a significant difference between the end of the year assessment scores for the students who were rewarded with candy (M=87.53) and the scores of the students who completed the end of the year assessments in the past five years (M=86.23, SD=7.5); z=0.95, p=0.34, d=0.17.
Additional Helpful Resources:
Additional Helpful Resources:
References
Morrow, J. (n.d.). One-sample z-test - SPSS (Part 1). Retrieved from http://www.how2stats.net/2014/03/one-sample-z-test.html
Salkind, N. J. (2017). Statistics for people who (think they) hate statistics (6th ed.). Washington, DC: Sage Publications.
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