A one-sample t-test for the mean is a type of hypothesis test that is used with quantitative variables (one quantitative variable) to determine whether a sample comes from a population with a specified mean. Not quite. The test is not about the sample. The test is to ascertain whether the population is likely to have a specified mean. Sometimes the population mean is not known, so it will instead be a hypothesized mean. Sometimes?  It compares the difference between the observed statistic and a hypothesized value to the standard error of the observed statistic.  This is too technical for the first paragraph. Take another paragraph to get into the details. This can be expressed with the equation

The assumptions and conditions for the one-sample t-test for the mean are the same as for the one-sample t-interval: random, 10%, and nearly normal. Don't frame this in terms of something else. There is already a page for the interval. Just state what the conditions are for this test. If the conditions are met, we can proceed with the test.  

The t-value can be interpreted the same as a p-value. This is not correct. The t-score plays the same role as the z-score did for the one-proportion test. If t< 0.05, we reject the null hypothesis, and accept the alternate hypothesis.  Therefore, if t > 0.05, we fail to reject the null hypothesis, and reject the alternate hypothesis because we have insufficient evidence to suggest otherwise.  These should be P, not t.

Other than some conceptual misunderstandings, this is a pretty good intro.

No need for an extra header here. Look at the sample page (Clustered bar graph) to see how to transition smoothly into the example.

Example:

A nutritional guide book has claimed that the mean calorie content of Plain Vanilla Yogurt available in stores is 120. So accordingly we have collected some samples from the local grocery store to see if this is true. So we set up our hypothesis like so:

     (This reflects our hypothesis that the mean of the yogurts calories will be 120)

      (This reflects our alternative hypothesis that the mean will not fall at 120 calories)

After this, your exposition severely breaks down. Use full sentences (with punctuation!) and full paragraphs.

Check conditions:  Random, 10%, and nearly normal (if sample size is less than 40, check QQ-plot/Histogram) Don't just state conditions. Check them!

Mechanics - Find and interpret the t-score using the formula

Be sure to comment on where all these numbers come from.

Because the t-score is greater than 0.05 we fail to reject the null hypothesis that the mean vanilla yogurt will have a calorie count of 120.  We also do not have sufficient evidence to prove our alternative hypothesis that it does not equal 120, so we reject the alternative hypothesis as well. None of this makes sense. You have no P-value, so you can't reach a conclusion. When you do, you either reject the null or fail to reject the null. You can't reject the alternative hypothesis.

SPSS can also perform these same mechanics, with less room for error.  The output below shows the same t-score of 1.554.

Generating a one-sample t-test for the mean in SPSS

• Go to the "Analyze" menu, hover over "Compare Means" to see a drop down menu, and select "One-Sample T Test". You don't need to tell the user how to use their mouse.
• Drag the quantitative variable that you are testing to the "Test Variable(s)" box.
• Change the "Test Value" to the hypothesized value for your data, because this is the value that is being testing. Be more specific. It's the null hypothesis value that goes here. 
• Do not change any other options. Then there's no reason to say this.
• Click "OK".
• The "One-Sample Statistics" chart and "One-Sample Test" chart will appear in the output window.
• In the "One-Sample Test" chart we can see our t value.  For the above example, t = 1.554. And also the degrees of freedom and the P-value.

The following video illustrates these steps: