There are three grades in a report card that you want to interpret in terms of performance: mathematics 75, english 85, and science 90. This means are 72,83 and 88, respectively. The standard deviation are 3, 10, and 15, respectively

There is no sufficient evidence to compare the grades in Math, English, and Science.

Step-by-step explanation:

Step 1:

Ho: There is no sufficient evidence to compare the grades in Math, English, and Science.

Ha: There is sufficient evidence to compare the grades in Math, English, and Science.

Step 2: Alpha level = 0.05

Step 3: Get the z-scores

Z1 = (75-72)/3 = 1.00

Z2 = (85-83)/10 = 0.20

Z3 = (90-88)/15 = 0.13

Step 4: Get the critical value and compare the z-scores with the critival value

0.05/2 = 0.025 (Divide 2 for two-tailed).

So, 0.5 - 0.025 = 0.4750 (0.5 is half of the curve).

Find this 0.4750 in the table of standard normal curve.

We can see that 0.4750 falls in 1.96. That is positive/negative 1.96.

We may draw the bell-curve to see the image and numbers clearly.

Step 5: Conclusion

Because the computed test statistics, z=1.00, 0.20, and 0.13 for Math, English, and Science respectively), fall within the non-rejection region (within positive/negative 1.96, which is the critical value), accept the null hypothesis. Thus, There is no sufficient evidence to compare the grades in Math, English, and Science.