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Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is mu Subscript dequals0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.
Start 3 By 10 Table 1st Row 1st Column Subject 2nd Column Upper A 3rd Column Upper B 4st Column Upper C 5st Column Upper D 6st Column Upper E 7st Column Upper F 8st Column Upper G 9st Column Upper H 10st Column Upper I 2nd Row 1st Column Before 2nd Column 168 3rd Column 180 4st Column 157 5st Column 132 6st Column 202 7st Column 124 8st Column 190 9st Column 210 10st Column 171 3rd Row 1st Column After 2nd Column 162 3rd Column 178 4st Column 145 5st Column 125 6st Column 171 7st Column 126 8st Column 180 9st Column 195 10st Column 163 EndTable



Answer :

nahasmilana

To compute the value of the t-test statistic for testing the claim that the paired sample data comes from a population where the mean difference is μd​=0, we need to follow these steps:

1. Calculate the Mean Difference (dˉ): Calculate the difference for each pair of data points (After - Before) and then find the mean of these differences. Mean Difference (dˉ)=Number of Data Points∑Differences​

2. Calculate the Standard Deviation of the Differences (sd​): Calculate the standard deviation of the differences using the formula: sd​=√n−1∑(di​−dˉ)2​​

3. Calculate the Standard Error of the Mean Difference (SEdˉ​): The standard error of the mean difference is given by: SEdˉ​=√nsd​​

4. Calculate the t-Test Statistic: The t-test statistic is calculated as: t=SEdˉ​dˉ−μd​​ Given the data provided in the table, you need to calculate the mean difference, standard deviation of the differences, standard error of the mean difference, and then use these values to compute the t-test statistic using the formula mentioned above.

Remember to round intermediate calculations to four decimal places and final answers to three decimal places.