Running Head Respond To Questions 2 Respond To Questions 5

Running Head Respond To Questions2respond To Questions5respond

RESPOND TO QUESTIONS. 5 RESPOND TO QUESTIONS. Name: Institution: Instructor: RESPOND TO QUESTIONS. . On a standard measure of hearing ability, the mean is 300, and the standard deviation is 20. Provide the Z scores for persons whose raw scores are 340, 310, and 260. Provide the raw scores for persons whose Z scores are 2.4, 1.5, and -4.5.

Calculate the Z scores for raw scores 340, 310, and 260:

- Z = (raw score – mean) / standard deviation

- For 340: Z = (340 – 300) / 20 = 40 / 20 = 2.0

- For 310: Z = (310 – 300) / 20 = 10 / 20 = 0.5

- For 260: Z = (260 – 300) / 20 = -40 / 20 = -2.0

Calculate the raw scores for Z scores 2.4, 1.5, and -4.5:

- Raw score = mean + (standard deviation * Z)

- For Z=2.4: Raw = 300 + (20 * 2.4) = 300 + 48 = 348

- For Z=1.5: Raw = 300 + (20 * 1.5) = 300 + 30 = 330

- For Z=-4.5: Raw = 300 + (20 * -4.5) = 300 - 90 = 210

Using the unit normal table, find the proportion under the standard normal curve that lies to the right of each Z:

- For Z=1.00: Area to right = 1 – 0.8413 = 0.1587

- For Z=-1.05: Area to right = 0.5 + 0.3531 = 0.8531

- For Z=0: Area to right = 0.5 + 0 = 0.5

- For Z=2.80: Area to right = 1 – 0.9974 = 0.0026

- For Z=1.96: Area to right = 1 – 0.9750 = 0.0250

Assuming the scores of architects on a creativity test are normally distributed, determine the percentage of architects with Z scores above and below specific values:

- Above 0.10: 1 – 0.5398 = 0.4602 → 46.02%

- Below 0.10: 0.5398 → 53.98%

- Above 0.20: 1 – 0.5793 = 0.4207 → 42.07%

- Below 0.20: 0.5793 → 57.93%

- Above 1.10: 1 – 0.8643 = 0.1357 → 13.57%

- Below 1.10: 0.8643 → 86.43%

- Above -0.10: 1 – 0.4602 = 0.5398 → 53.98%

- Below -0.10: 0.4602 → 46.02%

A statistics instructor wants to measure the effectiveness of teaching skills in a class of 102 students using systematic sampling:

- This sampling method is systematic, not purely random, because students are selected at regular intervals (every third student) starting from a random point (Thompson, 2013).

- Number of students sampled = total students / interval = 102 / 3 = 34 students.

To conduct a survey of visitors on campus to obtain a representative sample:

- The best approach is simple random sampling because:

- Each visitor has an equal chance of being selected, reducing selection bias (Jackson, 2012).

- It ensures the sample accurately reflects the population, facilitating generalizations.

References

- Heiman, G. W. (2011). Basic statistics for the behavioral sciences. Belmont, CA: Wadsworth Cengage Learning.

- Jackson, S. L. (2012). Research methods and statistics: A critical thinking approach. Belmont, CA: Wadsworth Cengage Learning.

- Thompson, S. K. (2013). Sampling. Hoboken, N.J: Wiley.