Test of Hypothesis

Vidhyamath Online

Instructor

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The means of two single-large samples of 1000 and 2000 members are 67.5 inches and 68.0 inches respectively. Can the samples be regarded as drawn from the same population of standard deviation 2.5 inches? (Test at 5% level of significance.)

  • 17 Apr, 2025
Replies (4)
Vidhyamath Online

Instructor

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Concepts:

Hypothesis testing, Two sample means, Z-test

Explanation:

To determine if the two samples can be regarded as drawn from the same population, we will perform a two-sample Z-test for means. The null hypothesis (H0) states that the means are equal, while the alternative hypothesis (H1) states that they are not equal. We will use the following formula for the Z-test:where  and  are the sample means,  is the population standard deviation, and  and  are the sample sizes.

Step by Step Solution:

Step 1: Hypothesis setting

null hypothesis (H0: µ1 = µ2)

and the alternative hypothesis (H1: µ1 ≠ µ2).

Test Statistics

Step 2

Calculate the difference between the sample means: .

Step 3

Calculate the standard error (SE): 

Step 4

Calculate the Z statistic: .

Level of Significance

Step 5

Compare the Z statistic with the critical value for a two-tailed test at the 5% significance level (approximately ±1.96). Since -5.17 < -1.96, we reject the null hypothesis.

Conclusion:

The samples cannot be regarded as drawn from the same population.

  • 17 Apr, 2025

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