Question 1207795: You wish to test the following claim (Ha)at a significance level of a=0.004.
You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:
data
54.9
51.5
61.5
66.5
68.2
71.5
76.5
74.9
77.9
91.5
81.5
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! **1. Calculate Sample Mean and Standard Deviation**
* **Sample Mean (x̄):**
(54.9 + 51.5 + 61.5 + 66.5 + 68.2 + 71.5 + 76.5 + 74.9 + 77.9 + 91.5 + 81.5) / 11
= 69.27
* **Sample Standard Deviation (s):**
Use a calculator or statistical software to calculate the sample standard deviation.
s ≈ 11.783
**2. Calculate the t-statistic**
* **Formula:**
t = (x̄ - μ₀) / (s / √n)
where:
* x̄ is the sample mean (69.27)
* μ₀ is the hypothesized population mean (you did not provide this value - please specify the value of μ₀ for the accurate calculation)
* s is the sample standard deviation (11.783)
* n is the sample size (11)
* **Example:**
* Let's assume the hypothesized population mean (μ₀) is 60.
* t = (69.27 - 60) / (11.783 / √11)
* t ≈ 2.618
**3. Calculate the p-value**
* **Degrees of Freedom:** df = n - 1 = 11 - 1 = 10
* **Using a t-distribution table or statistical software:**
* Find the p-value associated with the calculated t-statistic (2.618) and degrees of freedom (10).
* **Note:** Since you did not specify the direction of the alternative hypothesis (Ha), we will assume a two-tailed test.
* **Example:**
* If t = 2.618 and df = 10, the p-value for a two-tailed test is approximately 0.0272.
**Therefore:**
* **test statistic = 2.618 (assuming μ₀ = 60)**
* **p-value = 0.0272 (assuming μ₀ = 60 and a two-tailed test)**
**Important Notes:**
* **Hypothesized Mean (μ₀):** You must specify the hypothesized population mean (μ₀) to accurately calculate the t-statistic and p-value.
* **Software:** Use statistical software (like R, Python, Excel, or SPSS) to perform these calculations more efficiently and accurately.
* **Interpretation:** If the p-value is less than the significance level (α = 0.004), you would reject the null hypothesis. If the p-value is greater than or equal to α, you would fail to reject the null hypothesis.
This analysis provides a framework for conducting the t-test. Remember to adjust the calculations based on the specific hypothesized population mean (μ₀) for your analysis.
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