Instruction of online calculator
One Sample T Test Calculator
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One Sample T Test Calculator Instruction Guide
Introduction
The One Sample T Test Calculator is a statistical tool designed to assess whether the mean of a sample differs significantly from a specified population mean (μ0). This test is commonly used when the population standard deviation is unknown, requiring the use of the sample standard deviation instead.
The test helps determine if there is enough statistical evidence to support an alternative hypothesis ((H_1)), which proposes that the sample mean is not equal to, greater than, or less than the population mean.
How to Use
- Input Data Selection
Choose the appropriate input type based on the available statistical measures:- Unknown Statistics Measures: Provide the list of all sample data ((x)), population mean (μ0), and significance level (a).
- Known Statistics Measures: Enter the sample mean, sample standard deviation, sample size (n), population mean (μ0), and significance level (a).
- Known t-score: Input the significance level (a), calculated t-score, and sample size (n).
- Alternative Hypothesis Selection
Choose the form of the alternative hypothesis ((H1)):- Two-tailed test: (μ ≠ μ0) (The sample mean is significantly different from the population mean.)
- Left-tailed test: (μ < μ0) (The sample mean is significantly lower than the population mean.)
- Right-tailed test: (μ > μ0) (The sample mean is significantly higher than the population mean.)
- Calculation
The calculator computes the t-score based on the provided data and compares it with the critical t-value determined by the significance level and degrees of freedom ((df = n-1)). - Interpret Results
The output provides:- t-score: The computed value used to assess the hypothesis.
- Decision: The calculator states whether the null hypothesis ((H0)) can be rejected or not, based on the significance level (a). If the probability of rejection is lower than (a), (H0) is rejected; otherwise, it is accepted.
Examples for Each Input Data Selection
1. Unknown Statistics Measures Example
Given Input Data:
- Sample Data: (x = [12, 15, 14, 10, 18, 17, 16, 13, 19, 11])
- Population Mean (μ0) = 14
- Significance Level (a) = 0.05
- Alternative Hypothesis: (μ ≠ μ0 ) (Two-tailed test)
Calculation:
- Compute Sample Mean ((\bar{x})):
x̄ = {12 + 15 + 14 + 10 + 18 + 17 + 16 + 13 + 19 + 11}/{10} = 14.5 - Compute Sample Standard Deviation (s):
s = 3.13 - Compute t-score:
t = (14.5 – 14)(3.13 / √10 )= 0.506
Output:
- t-score: 0.506
- Result: Cannot accept (H1) with the probability of (1 – a). The evidence does not support rejecting (H0) at the given significance level.
The output of online solver for this example is as follows:
2. Known Statistics Measures Example
Given Input Data:
- Sample Mean (x̄) = 15.2
- Sample Standard Deviation (s) = 3.5
- Sample Size (n) = 25
- Population Mean (μ0) = 14
- Significance Level (a) = 0.05
- Alternative Hypothesis: (μ ≠ μ0 ) (Two-tailed test)
Calculation:
t=(x̄-μ0)/(s/√n)=(15.2-14)/(3.5/5)=1.714
Output:
- t-score: 1.714
- Result: Cannot accept (H1) with the probability of (1 – a). The evidence does not support rejecting (H0) at the given significance level.
The output of online solver for this example is as follows:
3. Known t-score Example
Given Input Data:
- Significance Level (a) = 0.05
- t-score = 1.45
- Sample Size (n) = 20
- Alternative Hypothesis: (μ > μ0) (Right-tailed test)
Decision Rule:
- Compare the given t-score (1.45) with the critical t-value at (a= 0.05) with ( df = n-1 = 19 ).
- The critical t-value for (a= 0.05) in a right-tailed test is approximately 1.729.
- Since ( t = 1.45 < 1.729 ), the null hypothesis ((H0)) is not rejected.
Output:
- t-score: 1.45
- Result: Cannot accept (H1) with the probability of (1 – a). The evidence does not support rejecting (H0) at the given significance level.
The output of online solver for this example is as follows:
Each example illustrates a different input scenario for performing the One Sample T Test. Let me know if you need adjustments!