Part 1:

Use the IQ variable, choose 10 scores, in the Howell Excel Data Set and transform the x values into z-scores using the = 90 with = 17. Then put all information in a table using the "

You need to compare the IQ, the same 10 scores, to the national average of = 100 with = 15 for the students in the math class. Add another column to your chart, using the "

Part 2:

Then, in

Explain the reasons why transforming x values into z-scores is useful by using the example of the problem you solved in Part 1. Your explanation should include:

Why knowing the z-scores for IQ helps you to understand the standard normal distribution of these scores for the math class.

How z-scores can help researchers use the data from a sample to make inferences about a population.

How converting the IQ scores (x-score) to the more familiar metric IQ scores (z-scores) in the second column can be helpful for the students in the math class.

https://docs.google.com/spreadsheets/d/1yVefKmoy1CLMhnBuFQuos818Agj-3YUp/edit?usp=sharing&ouid=100358846662393356565&rtpof=true&sd=true

Answerand explanations

Part 1:

X	Z-score ( = 90, = 17)	Z-score ( = 100, = 15)
94	0.235	-0.4
89	-0.059	-0.733
128	2.235	1.867
74	-0.941	-1.733
114	1.412	0.933
55	-2.059	-3
98.93	0.525	-0.071
82	-0.471	-1.2
119	1.706	1.267
123.5	1.971	1.567

Part 2:

z-scores of IQ is a standard score that describes the position of a raw score (x-scores) in terms of its distance from the mean () when measured in the standard deviation ().

The z-score is helpful for researchers in finding probabilities.

z-scores are helpful for comparing different distributions with different mean and standard deviations.

Step-by-step explanation

The following are the 10 IQ scores.

94, 89, 128, 74, 114, 55, 98.93, 82, 119, 123.5

Let X : IQ scores

Part 1:

The formula for z-scores is,

Find z-scores using = 90 and = 17 and using =100 and = 15.

X	Z-score	Z-score
94
89
128
74
114
55
98.93
82
119
123.5

Part 2:

z-scores of IQ is a standard score that describes the position of a raw score (x-scores) in terms of its distance from the mean () when measured in the standard deviation ().

For example, for = 90 and = 17 the z-score for X =94 is 0.235. This indicates that the X is at distance 0.235 from the mean IQ score.

The z-score is helpful for finding probabilities. The x-score is converted to a z-score and using standard normal distribution the probability for z-score can be computed.

For example, the probability that the IQ is less than 94 is computed by using the z-score. The z-score for x = 94 is 0.235.

Therefore, P(z < 0.235) = 0.592

z-scores are helpful for comparing different distributions with different mean and standard deviations.

For the given example there are two distributions with = 90 and = 17 and = 100 and = 15.

For x-score 94, the z-score for the first distribution is 0.234, here the positive sign indicates that the score is 0.234 units above the mean and for the second distribution is -0.4, which indicates that the score is 0.4 units below the mean.

Converting the IQ scores to z-scores will help students in comparing their scores with the national average.

Is this answer helpful?

Your feedback will help us provide a better solution

Collapse

GOODMATCH

A math class took the IQ score (i.e., IQ) test. It was found that the group average IQ variable in the Howell Excel Data Set had a = 90 with = 17 for the math class. To find out the relative location of each of the IQ scores within this distribution, you simply convert your test scores into z-scores. Choose 10 IQ Scores to find the z-scores.

Part 1:

Use the IQ variable, choose 10 scores, in the Howell Excel Data Set and transform the x values into z-scores using the = 90 with = 17. Then put all information in a table.

You need to compare the IQ, the same 10 scores, to the national average of = 100 with = 15 for the students in the math class.

Part 2:

• Explain the reasons why transforming x values into z-scores is useful by using the example of the problem you solved in Part 1. Your explanation should include:
  • Why knowing the z-scores for IQ helps you to understand the standard normal distribution of these scores for the math class.
  • How z-scores can help researchers use the data from a sample to make inferences about a population.
  • How converting the IQ scores (x-score) to the more familiar metric IQ scores (z-scores) in the second column can be helpful for the students in the math class.

Answerand explanations

Detailed answer on photo. Hope you appreciate my effort. Thank you.

Step-by-step explanation

Is this answer helpful?

Your feedback will help us provide a better solution

Collapse