Please help!!4 A researcher aims to determine if there is a difference in manual dexterity between athletes and band members. Two random samples of 22 participants each are tested for manual dexterity. The athletes' mean score is 87, while the band members' mean score is 93. The test's population standard deviation is 7.6. With a significance level of \( \alpha = 0.05 \), the question is whether a significant difference exists in the mean scores. The P-value method is used for this hypothesis test.**Part 1 of 5****Hypotheses and Claims:**- Null Hypothesis (\( H_0 \)): \( \mu_1 = \mu_2 \) (no difference in means; not the claim)- Alternative Hypothesis (\( H_1 \)): \( \mu_1 \neq \mu_2 \) (difference in means; claim)This is a two-tailed hypothesis test.**Part 2 of 5**The calculated test value is \( z = 2.2 \). Intermediate steps should be rounded to four decimal places, and the z-score values should be rounded to two decimal places.**Part 3 of 5**The computed P-value is 1.266, rounded to four decimal places. **Educational Website Transcription:****Statistical Analysis Exercise****Part 2 of 5**- **Task:** Compute the test value. - **Instructions:** Round all intermediate steps to four decimal places and always round z-score values to two decimal places. - Calculated z-score: \( z = 2.2 \)**Progress Indicator:** Partial progress bar shown with "Part: 2 / 5" completed.**Part 3 of 5**- **Task:** Compute the \( P \)-value. - **Instructions:** Round the answer to four decimal places. - Calculated \( P \)-value: \( P = 1.266 \)**Progress Indicator:** Partial progress bar shown with "Part: 3 / 5" completed.**Part 4 of 5**- **Task:** Make the decision based on the hypothesis test.- **Instructions:** Choose the appropriate action regarding the null hypothesis. - **Option Dropdown:** (Choose one)**Progress Indicators:**- Each section is accompanied by a horizontal progress bar, showing the completion status of the respective part in the exercise.

Given information: n1=22n2=22x¯1=87x¯2=93α=0.05σ1=7.6σ2=7.6 Find: State the decision of the test.

A researcher wishes to see if there is a difference in the manual dexterity of athletes and that of band members. Two random samples of 22 are selected from each group and are given a manual dexterity test. The mean of the athletes' test was 87, and the mean of the band members' test was 93. The population standard deviation for the test is 7.6. Use u₁ for the mean of the athletes' test. At a = 0.05, is there a difference in the mean scores? Use the P-value method and tables. Part: 0/5 Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. Ho: H₁ H₂ not claim H₁ H₁ H₂ claim Part: 1/5 This hypothesis test is a two-tailed Part 2 of 5 2= 2.2 Part: 2/5 ▼ Part 3 of 5 ▼ X S test. Compute the test value. Round all intermediate steps to four decimal places and always round z score values to two decimal places. 0<0 >O 0=0 X X Hy Compute the P-value. Round the answer to four decimal places. P-value = 1.266 Ś H₂