Open the following data set. The set contains 75 scores which represent typing speed in words per minute for 3rd and 4th grade students. The data consists of 39 3rd grade students and 36 4th grade students. We will explore the following hypotheses:

• H₀: Typing speeds do not vary between 3rd and 4th grade
• H₁: There is a difference between typing speed among 3rd and 4th grade students.

The population mean (μ) is 11.48. The population standard deviation (σ) is 6.77.

We will use the 4th grade scores as the sample to see if they differ from the population mean. The sample mean (x̅) is 14.14

We now have all of the information we need to compute the z-score.

We will start by subtracting the population mean from the sample mean: 14.14 - 11.48 = 2.66

We will then take the square root of the sample size of 36. This equals: 6

We then divide the population standard deviation of 6.77 by 6, which equals 1.13

Finally, divide 2.66 by 1.13, which equals the Z-score of 2.35

We will refer back to the Z-table for Positive Values

0.4906 this represents that the values of the sample mean are within the are under that curve that is 49.06% above the mean, see graph below for visual approximation (the graph indicates a shaded area of 98.97%, which is close to our 49.06% added to the area below the mean(50%) the meaning of the z-score is evident in the graph, as it shows approximately the point that is 2.25 standard deviations from the population mean):