Answer to Question #297369 in Statistics and Probability for Lian

Question

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.

Answer 1

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.