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LAB REPORT 5: 1-Sample t-Test (Data in Column)
Objective
To perform a 1-Sample t-Test using raw data stored in a column in Minitab to assess whether
the sample mean differs significantly from the hypothesized population mean when the
population standard deviation is unknown.
Introduction
The 1-Sample t-Test is used when the population standard deviation (σ) is unknown, and the
sample standard deviation (s) is used instead. This test is especially useful for small sample
sizes (n<30), though it can be applied to larger datasets as well. It is often employed when
analysing sample data to test hypotheses about population means.
The formula for the 1-Sample t-Test is:
Where:
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X bar = Sample Mean
μ = Hypothesized Population Mean
s = Sample Standard Deviation
n = Sample Size
The t-statistic follows a t-distribution with n−1degrees of freedom. The significance of the
test is determined by comparing the t-statistic to the critical values from the t-distribution, or
equivalently, by checking the p-value.
In this lab, we perform the 1-Sample t-Test using raw data entered into a column in Minitab,
allowing for automated calculations and statistical analysis.
Procedure
Steps for Performing a 1-Sample t-Test in Minitab Using Data in a Column:
1. Open Minitab and Input Data:
o
Open Minitab and enter the raw data (individual observations) into a column (e.g.,
C1).
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o
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Alternatively, import the dataset from an external source (e.g., Excel, CSV).
2. Navigate to the t-Test Tool:
o
Click on Stat → Basic Statistics → 1-Sample t...
3. Select Data Input Option:
o
o
Choose Samples in Columns.
Specify the column containing the raw data (e.g., C1).
4. Enter Hypothesized Mean:
o
Input the Hypothesized Mean (μ). This is the population mean you want to test
against the sample mean.
5. Set Hypothesis Test Options:
o
o
Choose the alternative hypothesis direction (e.g., "less than," "greater than," or "not
equal").
Specify the significance level (typically α=0.05, unless specified otherwise).
6. Run the Analysis:
o
Click OK to perform the t-Test and generate the results.
7. Interpret the Results:
o
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Review the output, which will include the t-statistic, p-value, and confidence
intervals for the sample mean.
Compare the p-value with the significance level (α\alphaα) to decide whether to
reject or fail to reject the null hypothesis.
Example for t test:
The average amount of pesticide that is packed in canes is 6 liters. A random sample of 10 canes
showed the following data:
5.95
5.90
6.23
6.29
5.95
6.20
6.29
6.05
Test weather the process is in control at 1% level of significance.
Given Data:
𝐻0 : 𝜇 = 6 Liters
𝐻1 : 𝜇 ≠ 6 𝐿𝑖𝑡𝑒𝑟𝑠
sample size = n= 10
Level of Significance = 𝛼 = 0 ⋅ 01.
Confidence level = 1- 𝛼 = 1- 0.01 = 0.99 =99%
6.32
5.82
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Step 1 (Enter values and use 1-sample Z-test)
Step 2 ( Enter values)
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Step 3 (results)
Conclusion
Performing a 1-Sample t-Test using raw data in Minitab is an efficient way to test hypotheses
about population means when the population standard deviation is unknown. By entering data
into a column, Minitab automates the calculation of the t-statistic, degrees of freedom, and pvalue, simplifying the statistical analysis.
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This lab demonstrates how to use Minitab for hypothesis testing, providing clear insights into
the significance of the sample mean in relation to a hypothesized population mean. The use of
Minitab ensures accurate and quick analysis, which is crucial for making data-driven
decisions in various fields.