Question 3: IQ scores for 31 randomly selected grade 7 girls in a particular school district are as follows: IQ Score 114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93 Find the mean of the sample using Excel (include your Excel formula in your solutions). IQ scores typically follow a Normal distribution and are designed so that σ = 15. Using this information, compute three confidence intervals (90%, 95%, and 98%) for the mean IQ score and fill in the table below. Please show any computations needed to find the margin of Note: z-critical values (z*) are given at the bottom of Table C of your book. Confidence Level z-critical value Margin of Error Confidence Interval Length of Interval 90% 95% 98% What seems to be happening to the size of the interval as we increase our level of confidence?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Question 3: IQ scores for 31 randomly selected grade 7 girls in a particular school district are as follows:
| IQ Score |
| 114 |
| 100 |
| 104 |
| 89 |
| 102 |
| 91 |
| 114 |
| 114 |
| 103 |
| 105 |
| 108 |
| 130 |
| 120 |
| 132 |
| 111 |
| 128 |
| 118 |
| 119 |
| 86 |
| 72 |
| 111 |
| 103 |
| 74 |
| 112 |
| 107 |
| 103 |
| 98 |
| 96 |
| 112 |
| 112 |
| 93 |
- Find the mean of the sample using Excel (include your Excel formula in your solutions).
- IQ scores typically follow a
Normal distribution and are designed so that σ = 15. Using this information, compute three confidence intervals (90%, 95%, and 98%) for the mean IQ score and fill in the table below. Please show any computations needed to find the margin of
Note: z-critical values (z*) are given at the bottom of Table C of your book.
|
Confidence Level |
z-critical value |
Margin of Error |
Confidence Interval |
Length of Interval |
|
90% |
|
|
|
|
|
95% |
|
|
|
|
|
98% |
|
|
|
|
- What seems to be happening to the size of the interval as we increase our level of confidence?
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