8 Several students were tested for reaction times (in thousandths of a second) using their right and left hands. Each value is the elapsed time between the release of a strip of paper and the instant it is caught by the subject. Results from five of the students are included in the graph to the right. A 0.05 significance level is used to test the claim that there is no difference between the reaction times of the right and left hands.**Hypotheses:**Let \( \mu_d \) be the mean difference of the right and left hand reaction times. - \( H_0: \mu_d = 0 \) - \( H_1: \mu_d \neq 0 \) **Test statistic:**Calculate \( t = \) (Round to three decimal places as needed.)**Identify the critical value(s):** Select the correct choice and fill in the answer box.- \( A. \) The critical values are \( t = \) (Round to three decimal places.)- \( B. \) The critical value is \( t = \) (Round to three decimal places.)**Conclusion:**There is [enough/not enough] evidence to warrant rejection of the claim that there is [no/a] difference between the reaction times of the right and left hands.**Reaction Time Data Table:**| Right Hand | Left Hand ||------------|-----------|| 102 | 111 || 115 | 133 || 140 | 149 || 187 | 194 || 190 | 207 |**Graph Explanation:**- The graph plots reaction times for the right hand on the x-axis and the left hand on the y-axis.- The data points for each of the five students can be observed visually along the chart, showing the correlation between right and left hand reaction times. Each axis is scaled from 100 to 220.

The random variable is reaction time. There are two dependent samples which are right hand and left hand. We have to test whether there is no difference between the reaction times of the right and left hands or not. This is Paired t-test with two-tailed.Let μd be the mean of the differences of the right and left hand reaction times. The null and alternative hypotheses areEXCEL (Data Analysis) Procedure: Step 1: In EXCEL sheet, enter Right Hand in one column and enter Left Hand in one column. Step 2: In Data, select Data Analysis and choose t test: Paired Two-samples for Mean. Step 3: In Input Variable 1 Range: select Right Hand. Step 4: In Input Variable 2 Range: select Left Hand. Step 5: Select Lables. Click Ok. EXCEL (Data Analysis) Output: The value of the test statistic is t =-5.262.Critical region: (A). The critical values are t = ±2.776. There is enough evidence to warrant rejection of the claim that there is no mean difference between the reaction times of the right and left hands.

Math

Statistics

Several students were tested for reaction times (in thousandths of a second) using their right and left hands. (Each value is the elapsed time between the release of a strip of paper and the instant that it is caught by the subject.) Results from five of the students are included in the graph to the right. Use a 0.05 significance level to test the claim that there is no difference between the reaction times of the right and left hands E Click the icon to view the reaction time data table 160 100 150 Right Hnd What are the hypotheses for this test? Let be the V of the right and left hand reaction fimes. Reaction time data table H 70 What is the test statistic? Right Hand 102 Left Hand 1= (Round to three decimal places as needed.) 111 115 133 Identily the critical value(s). Select the correct choice below and fill the answer box within your choice (Round to three decimal places as needed) 140 149 187 194 OA. The critical values are t= 207 190 O B. The critical value is t= What is the condusion? Print Done There enough evidence to warrant rejection of the claim that there is V between the reaction times of the right and left hands