Sangeetha Pulapaka

The test statistic gives us an idea of how far away our sample result is from our null hypothesis. For a one-sample t test for a mean, our test statistics is:

t = \frac{statistic - parameter}{standard\hspace{1mm}error\hspace{1mm}of\hspace{1mm}statistic}.

= \frac{\overline{x}-\mu_{0}}{\frac{s_{x}}{\sqrt{n}}}

The statistic \overline{x} is the sample mean, and the parameter \mu_{0} is the mean from the null hypothesis. The standard error

 of the sample mean is s_{x} (the sample standard deviation) divided by the square root of n (the sample size).

Our statistic is the sample mean \overline{x} = 208m.

Our parameter is the mean from the null hypothesis, so we use \mu_{0} = 200 m.

The sample standard deviation is s_{x} = 25m.

Since Adam took a sample of 49 drives, we use n = 49.

Plugging these values in the test statistic formula, we get:

t= \frac{\overline{x}-\mu_{0}}{\frac{s_{x}}{\sqrt{n}}}

t= \frac{208-200}{\frac{25}{\sqrt{49}}} = 2.24.