Question 1174407: A sample of 400 Male is found to have a mean height 171.40cm.can it be reasonably regarded as a sample from Large population with mean height 171.20cm and standard deviation 3.3? Test at 5% level of significance
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to perform the hypothesis test:
**1. Set up the Hypotheses:**
* **Null Hypothesis (H0):** The sample mean is equal to the population mean (μ = 171.20 cm).
* **Alternative Hypothesis (H1):** The sample mean is not equal to the population mean (μ ≠ 171.20 cm). This is a two-tailed test.
**2. Determine the Significance Level:**
* The significance level (alpha) is given as 5% or 0.05.
**3. Calculate the Test Statistic (z-score):**
* We use the z-test because the population standard deviation is known and the sample size is large (n > 30).
* The formula for the z-score is: z = (x̄ - μ) / (σ / √n)
* x̄ = sample mean (171.40 cm)
* μ = population mean (171.20 cm)
* σ = population standard deviation (3.3 cm)
* n = sample size (400)
* z = (171.40 - 171.20) / (3.3 / √400) = 0.20 / (3.3 / 20) = 0.20 / 0.165 = 1.21
**4. Find the P-value:**
* Since this is a two-tailed test, we need to find the probability of getting a z-score as extreme as 1.21 or -1.21.
* Using a z-table or calculator, the p-value is approximately 0.225.
**5. Make a Decision:**
* Compare the p-value with the significance level (alpha).
* If p-value < alpha, reject the null hypothesis.
* If p-value ≥ alpha, fail to reject the null hypothesis.
* In this case, 0.225 ≥ 0.05, so we fail to reject the null hypothesis.
**6. Conclusion:**
* There is not enough evidence to conclude that the sample mean is significantly different from the population mean at the 5% significance level. Therefore, it can be reasonably regarded as a sample from the large population.
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