Question

Answers to this question will be "increase", "decrease", "stay the same" or "not enough information."

Assume you have two normally distributed samples, each with a sample size of 70. The Mean (StDev) of samples 1 and 2, respectively, are 300 (15) and 210 (8). Every single score in the first sample is higher than every score in the second sample. Assume all scores are whole numbers. If the highest score in the second sample is moved to the first sample...

1- What happens to the value of the z score of the new mean of sample 1, compared to the value of the z score of the old mean of sample 1 (before the one score was moved from sample 2)? (Assume z scores are only calculated on sample 1, and that the ‘before’ and ‘after’ calculations were done separately, using only the appropriate data.)

2- What happens to the z score of a person in sample 2 with a raw score of 205, compared to their original z score? (Assume z scores are only calculated on sample 2, and that the ‘before’ and ‘after’ calculations were done separately, using only the appropriate data.)

3- What happens to the z score of a person who originally had the second highest score in sample 2, compared to their original z score? (Assume z scores are only calculated on sample 2, and that the ‘before’ and ‘after’ calculations were done separately, using only the appropriate data.)

4- What happens to the standard deviation of all z scores for sample 1, compared to the original standard deviation of all z scores for sample 1? (Assume z scores are only calculated on sample 1, and that the ‘before’ and ‘after’ calculations were done separately, using only the appropriate data.)

5- What happens to the value of the z score of the person who was moved from sample 2 to sample 1? (Assume z scores are calculated on each sample separately (i.e., on sample 2 before and on sample 1 after the data point is moved), using only the appropriate data.)

Answer 1

Explanation:

Answer:

The answers to the question are as follows

1- Stay the same

2- Increase

3- Increase

4- Increase

5- Decrease

Step-by-step explanation:

The z score is given by

Where x = Raw score

μ = Sample mean

σ = Standard deviation of the sample

New mean of sample 2, <

New standard deviation of sample <

1- Stay the same

From the formula for calculating z score and for the mean, we have

, which is the same before and after the transfer due to the formula as the new mean is now subtracted from itself

2- Increase

The z score of a person with 205 in sample 2 before the transfer was negative as the mean was 210 and the standard deviation was 8

After the transfer, the mean value and or the standard deviation would reduce and the z score of the person with 205 would increase

3- Increase

The z- score of the person who originally had the second highest score in sample 2 would increase as the new mean and standard deviations would be lower while his value x remain the same

4- Increase

Standard deviation is given by

since n would increase and the mean would decrease, the standard deviation would increase

5- Decrease

From positive to negative

The z score is a signed fraction number which shows the deviation of a data point from the mean as a factor of the standard deviation. The z score of the person who moved was originally positive as it was the highest in sample 2.

In sample 1 however the z score of that person is the lowest and below the mean hence it would be negative

Answer 2

The answers to the question are as follows

1- Stay the same

2- Increase

3- Increase

4- Increase

5- Decrease

Explanation:

The z score is given by
`z = (x-\mu)/(\sigma)`

Where x = Raw score

μ = Sample mean

σ = Standard deviation of the sample

New mean of sample 2,
`\mu_(2New)` <
`\mu_(2)`

New standard deviation of sample
`\sigma_(2 New)` <
`\sigma_2`

1- Stay the same

From the formula for calculating z score and for the mean, we have

`z = (\mu -\mu)/(\sigma) = 0`, which is the same before and after the transfer due to the formula as the new mean is now subtracted from itself

2- Increase

The z score of a person with 205 in sample 2 before the transfer was negative as the mean was 210 and the standard deviation was 8

After the transfer, the mean value and or the standard deviation would reduce and the z score of the person with 205 would increase

3- Increase

The z- score of the person who originally had the second highest score in sample 2 would increase as the new mean and standard deviations would be lower while his value x remain the same

4- Increase

Standard deviation is given by

`\sigma = \sqrt{(Sum(x - \mu))/(n) }` since n would increase and the mean would decrease, the standard deviation would increase

5- Decrease

From positive to negative

The z score is a signed fraction number which shows the deviation of a data point from the mean as a factor of the standard deviation. The z score of the person who moved was originally positive as it was the highest in sample 2.

In sample 1 however the z score of that person is the lowest and below the mean hence it would be negative