# One Sample t-Test in Excel

## QI Macros Add-in Conducts t-Tests and Interprets Results

A one sample t-Test compares test data to a specific value. It helps determine if the sample is greater than, less than or equal to the value.

Note: Excel does NOT do one-sample t-tests; QI Macros adds this functionality.

### One Sample t-Test Example

QI Macros adds a new tab to Excel's menu. To conduct a t-test using QI Macros follow these steps:

Let's say you want to know if the life of a light bulb is greater than 2,500 hours. Take your sample and input the data in Excel.

1. Click and drag over the data to select it.
2. Next, click on the QI Macros Menu > Statistical Tools > F & t Tests, and then select "t-Test: one sample":
3. 4. QI Macros will prompt for a confidence level (default = 0.95) and a Test Mean (light bulb life is less than or equal to 2,500 hours) QI Macros will perform the calculations and interpret the results for you: In this example, p-value = 0.00016 and alpha = 0.05 (1 - .95 the confidence level). Since p < .05 we Reject the Null Hypothesis. The means are not the same.

Note: TInv means "T Inverse" and is used in calculating the upper and lower confidence intervals.

Interprets the Results for You: QI Macros compares the p value to alpha and tells you what that means. In the above example, QI Macros tells you to "Reject the Null Hypothesis because p < 0.05 (Means are Different).

Interactive Results: QI Macros lets you change the confidence level and test mean to see what impact those changes have on your results. See areas outlined in red for cells that can be changed.

### Interpreting the t-Test One-Sample Results Manually

So we develop a null hypothesis (H0) that light bulb life is less than or equal to 2,500 hours and the alternate hypothesis (Ha) that bulb life is greater than 2,500 hours:

• H0 <= 2,500 hours
• Ha > 2,500 hours

Now, conduct a test of light bulb life and enter the data into Excel.

QI Macros automatically interprets the results for you. However, here is some guidance if you want to do that yourself.

Since the null hypothesis is that bulb life is less than or equal to 2,500, this is a one-sided test. Therefore, use the one-tail values for your analysis:

 If Then t-Test statistic > critical value  (i.e. t > tcrit) Reject the null hypothesis t-Test statistic < critical value  (i.e. t < tcrit) Cannot Reject the null hypothesis p value < a Reject the null hypothesis p value > a Cannot Reject the null hypothesis

Note: The two-sided values would apply if our null hypothesis was that:
H0: mean = 2,500 hours

Since the t statistic > t critical (4.904 > 1.76131) and p value < a (0.000116 < 0.05), we can reject the null hypothesis that bulb life is less than or equal to 2,500.

We can say that we are 95% confident that the bulb life is greater than 2,500 hours.

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### Customer Service - Another t-Test One Sample Example

Let's say you want to know if wait times in a branch bank are not greater than three minutes at a 95% confidence level. Mystery shoppers routinely visit the branch and collect their wait time. This gives us the data we need to test the hypothesis.

Select your data and then "t-Test: one-sample" from QI Macros > F & t Tests: Answer the prompts: Confidence level .95 and test mean 3. • H0 <= 3 minutes
• Ha > 3 minutes

The one-sided p value < a (.039776 is less than 0.05 (1-0.95)), so we must reject the null hypothesis that bank wait times are less than or equal to 3 minutes.

We can say that we are 95% confident that wait times are greater than 3 minutes.

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