One of the categories of special education are children who are diagnosed with specific learning disabilities. A major difficulty for children with this diagnosis surrounds the skills of reading. A special education teacher is interested in knowing whether a new reading technique increases reading skills for children diagnosed with specific learning disabilities. She uses the WRAT as a way of measuring reading skills and the average for this test is 55. She takes a random sample of 12 children diagnosed with specific learning disability, employs her reading program with them and finds the following scores on the WRAT: 57, 55, 49, 56, 57, 58, 61, 50, 60, 61, 58, 56. Test the null hypothesis at the .01 level of significance.
One of the categories of special education are children who are diagnosed with specific learning disabilities. A major difficulty for children with this diagnosis surrounds the skills of reading. A special education teacher is interested in knowing whether a new reading technique increases reading skills for children diagnosed with specific learning disabilities. She uses the WRAT as a way of measuring reading skills and the average for this test is 55. She takes a random sample of 12 children diagnosed with specific learning disability, employs her reading program with them and finds the following scores on the WRAT: 57, 55, 49, 56, 57, 58, 61, 50, 60, 61, 58, 56. Test the null hypothesis at the .01 level of significance.
Given Information :
One of the categories of special education are children who are diagnosed with specific learning disabilities. A major difficulty for children with this diagnosis surrounds the skills of reading. A special education teacher is interested in knowing whether a new reading technique increases reading skills for children diagnosed with specific learning disabilities. She uses the WRAT as a way of measuring reading skills and the average for this test is 55.
She takes a random sample of 12 children diagnosed with specific learning disability, employs her reading program with them and finds the provided scores on the WRAT .
First calculate mean and standard deviation of the given scores :
The sample size is . The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:
| x | x2 | |
| 57 | 3249 | |
| 55 | 3025 | |
| 49 | 2401 | |
| 56 | 3136 | |
| 57 | 3249 | |
| 58 | 3364 | |
| 61 | 3721 | |
| 50 | 2500 | |
| 60 | 3600 | |
| 61 | 3721 | |
| 58 | 3364 | |
| 56 | 3136 | |
| Sum = | 678 | 38466 |
The sample mean is computed as follows:
Also, the sample variance is
Therefore, the sample standard deviation is
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