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z-test

This document provides an overview of the Z test for two sample means. It defines the Z test, outlines when it is used, and provides the formula and steps to conduct a hypothesis test using the Z test. An example problem is included that tests if there is a significant difference in average monthly family incomes between two neighborhoods using census data from random samples of 100 families each.

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Good Morning!  Prepared by: Aljon A. Casupanan (BSEd III – Compassion)
Today’s Lesson: Z Test (Two Sample Mean Test)
Z Test (Two Sample Mean Test) Z test can be used in: • Education • Business • Engineering
We need to: • Accept Ho and Reject Ha when: the p value is greater than the level of significance. (p value > 휶) • Accept Ha and Reject Ho when: the p value is less than the level of significance. (p value < 휶)
When do we use Z Test (Two Sample Mean)? When two separate samples are drawn at random. When testing whether the two samples are taken from a single population.
When do we use Z Test (Two Sample Mean)? It is necessary that the sample must be independent.
Steps In Hypothesis Testing (Z Test Two Sample Mean Test) Step 1:State the null and alternative hypotheses Step 2: Identify or select the level of significance and the p - value Step 3: Compute the test statistic Step 4: Decision,whether to accept the null hypothesis (Ho) and reject alternative hypothesis (Ha) or vice versa Step 5: State the conclusion.
Formula in Computing the Test Statistic Using Z Test (Two Sample Mean Test) • when the given means are sample means. 풛 = 풙₁ − 풙₂ 풔₁² + 풏₁ 풔₂² 풏₂ • when the given means are population means. 풛 = 흁₁ − 흁₂ 흈₁² + 풏₁ 흈₂² 풏₂ 풙₁ = mean of the 1st sample 풙₂ = mean of the 2nd sample 흁₁ = mean of the 1st population 흁₂ = mean of the 2nd population 퐬₁ = standard deviation of the 1st sample 퐬₂ = standard deviation of the 2nd sample 흈₁ = standard deviation of the 1st population 흈₂ = standard deviation of the 2nd population 풏₁ = size of the 1st sample or population 풏₂ = size of the 2nd sample or population
We need to: • Accept Ho and Reject Ha when: the p value is greater than the level of significance. (p value > 휶) • Accept Ha and Reject Ho when: the p value is less than the level of significance. (p value < 휶)
Problem 1: Example 1. A bank is opening a branch in one of two neighborhoods. One of these factors considered by the bank was whether the average monthly family income (in thousand pesos ) in the two neighborhoods differed. From census records, the bank drew two random samples of 100 families and obtained the following information: Sample A Sample B 퐱 ₁ = ퟏퟎ, ퟏퟎퟎ 퐱 ₂ = ퟏퟎ, ퟑퟎퟎ s₁ = 300 s₂ = 400 n₁ = 100 n₂ = 100 The bank wishes to test the null hypothesis that the two neighborhoods have the same mean income. What should the bank conclude using 휶 = ퟎ. ퟎퟓ?
Problem 2: • An examination is given to 2 classes containing 40 and 50 students respectively. In the first class, the mean grade was 74 with a standard deviation of 8, while in the second class the mean grade was 78 with a standard deviation of 7. Is there a significant difference between the performance of the 2 classes at 0.05 significance level?
QUIZ #2
Answer the following: (Show your step by step solutions in numbers 1 and 2) 1. .The mean height of 50 male students who showed above average participation in college athletics was 68.2 inches with a standard deviation of 2.5 inches while 50 male students who showed no interest in such participation had mean height of 67.5 inches and a standard deviation of 2.8 inches. Test the hypothesis that male students who participated in college athletics are taller than other male students at 0.05 level of significance. (15 points)
• 2. The IQs of 16 students from one area of the city showed a mean of 107 with a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 with a standard deviation of 8.Is there a significant difference between the IQs of the two groups?Use 0.01 level of significance. (15 points)
3. How does z test (one sample mean) differ from z test (two samplemean)? (3 points) 4. How can we apply or use z test (two sample mean) in our real lives? (2 points)
z-test