What test can be used to test the difference between two sample means when the population variances or population standard deviations are known?
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In statistics, a two-sample z-test for means is used to determine if the means of two populations are equal. This test is used when the population standard deviations are known. As data scientists, it is of utmost importance to be able to understand and conduct this test accurately. This blog post will provide a detailed explanation of the two-sample z-test for means, as well as examples to help illustrate how it is used.
What is a two-sample Z-test for means?Two-sample Z-test for means is a statistical hypothesis testing technique that is used to determine if the difference between the two population means is not statistically significant. This test is used when the standard deviations (σ) of the two populations are known. This test can be used when we have a sample from each population and we know the variance for these populations. Here are some of the real-world examples where a two-sample z-test for means can be used:
Formula: Two-sample Z-test for means?The following is the formula for a two-sample z-test for means: x̄1 is the mean of the first sample x̄2 is the mean of the second sample μ1 is the mean of the first population μ2 is the mean of the second population (μ1 – μ2) is hypothesized difference between the population means σ1 is the standard deviation of the first population σ2 is the standard deviation of the second population n1 is the number of the data points in the first sample n2 is the number of the data points in the second sample Example: Two-sample Z-test for MeansA company wanted to compare the performance of its call center employees in two different centers located in two different parts of the country – Hyderabad, and Bengaluru, in terms of the number of tickets resolved in a day (hypothetically speaking). The company randomly selected 30 employees from the call center in Hyderabad and 30 employees from the call center in Bengaluru. The following data was collected: Hyderabad: x̄1 = 750, σ1 = 20 Bengaluru: x̄2 = 780, σ2 = 25 The company wants to determine if the performance of the employees in Hyderabad is different from the performance of the employees in the Bengaluru center. To do this, we will use a two-sample z-test for means. First, we will formulate the null and alternate hypotheses and set the level of significance for the test. H0: There is no difference between the performance of employees at different call centers. H1: There is a difference in the performance of the employees. The level of significance is set as 0.05. Next, the mean and standard deviation for each sample will need to be determined. Hyderabad: x̄1 = 750, σ1 = 20 Bengaluru: x̄2 = 780, σ2 = 25 Next, we will calculate the hypothesized difference between the two population means. In this case, the company is hypothesizing that the mean performance in Hyderabad is the same as that of Bengaluru. So, (μ1 – μ2 ) = 0 Finally, we will use the formula for two-sample z-test for means to calculate the test statistic. z= (x̄1 – x̄2 ) / √((σ1 )²/n1 + (σ2)²/n2) z = (-30) / √((20)²/30 + (25)²/30)) z = -5.13 At a significance level of 0.05, the p-value is less than 0.00001. You can calculate the same by using P-value from Z-score calculator. As the p-value is lot less than the critical value of 0.05, the result is statistically significant and hence you can reject the null hypothesis. Hence, the performance of Hyderabad’s team is considered to be not equal to the performance of Bengaluru’s team. SummaryWhen two samples are taken from two populations, the two-sample z-test for means is used to determine whether or not there is a significant difference between the two means. The null hypothesis states that there isn’t any statistical significance between the two population means (H0) and the alternate hypothesis says otherwise (H1). In order to perform the hypothesis testing to determine whether the difference exists between the two groups or samples and that the difference is statistically significant, the two-samples Z-test for means is used.
I have been recently working in the area of Data analytics including Data Science and Machine Learning / Deep Learning. I am also passionate about different technologies including programming languages such as Java/JEE, Javascript, Python, R, Julia, etc, and technologies such as Blockchain, mobile computing, cloud-native technologies, application security, cloud computing platforms, big data, etc. For latest updates and blogs, follow us on Twitter. I would love to connect with you on Linkedin. Check out my latest book titled as First Principles Thinking: Building winning products using first principles thinking Ajitesh KumarI have been recently working in the area of Data analytics including Data Science and Machine Learning / Deep Learning. I am also passionate about different technologies including programming languages such as Java/JEE, Javascript, Python, R, Julia, etc, and technologies such as Blockchain, mobile computing, cloud-native technologies, application security, cloud computing platforms, big data, etc. For latest updates and blogs, follow us on Twitter. I would love to connect with you on Linkedin. Check out my latest book titled as First Principles Thinking: Building winning products using first principles thinking What test can be used to test the difference between two sample means when the population variances and standard deviations are known?A z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large. A z-test is a hypothesis test in which the z-statistic follows a normal distribution.
What test can be used to test the difference between two means when the population standard deviation is unknown?The test comparing two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch t-test.
What test will be used if you test differences between two sample mean when the population mean is given?A t-test is an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related. T-tests are used when the data sets follow a normal distribution and have unknown variances, like the data set recorded from flipping a coin 100 times.
Which test is used to calculate differences in two means of population?Hypothesis test for the difference between means of two populations.
What is zA z-test, like a t-test, is a form of hypothesis testing. Where a t-test looks at two sets of data that are different from each other — with no standard deviation or variance — a z-test views the averages of data sets that are different from each other but have the standard deviation or variance given.
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