Hi friends! If you are looking for information on hypothesis testing using a one-sample t-test, you are on the right platform. This article explains the one-sample t-test with a solved example.
Criteria for selecting 1- sample T test.
- Data must be variable.
- Data is approximately normally distributed.
- A one-sample t-test is a useful statistical tool when you have a sample and want to assess whether its mean is significantly different from a known or hypothesized population mean.
- Formulate Hypothesis. (H1: Alternate Hypothesis & H0: Null Hypothesis)
Let us understand with an example.
Example: The time to repair an electronic instrument is a normally distributed random variable measured in hours. The repair times (in Hrs.) for 16 such instruments, chosen at random, are as follows.
159 280 101 212
224 379 179 264
222 362 168 250
149 260 485 170
Does it seem reasonable that the true mean repair time is greater than 250 hours ?
Information Given
- Normal distribution
- Data type – variable (Time)
- Sample size – 16
- Comparing sample mean with hypothesized population mean.
The above test is for the average. Note: We will conduct a one-sample t-test because we are selecting one sample and comparing it with a constant. In this case, it is crucial to formulate the Null Hypothesis (H0) and the Alternative Hypothesis (H1).
H1: µ > 250 Hours
H0: µ = 250 Hours
Now, we perform this test in Minitab.
Path
Stat>Basis statics >1-sample T- Test
Check the box (Tick) perform hypothesis test as shown in the above picture. Then go the Option tab.
Next, set the confidence level to 95.0 and choose the Alternative Hypothesis by selecting.
‘mean > Hypothesized mean.’ Click ‘Ok.’ Now, we obtain the p-value, which is 0.632. Consequently, we cannot reject the null hypothesis (H0), and we accept H0, indicating that H0: µ = 250 Hours.
The question posed was whether the true mean repair time is greater than 250 hours?
The answer is NO.