I just need help with d,e,fi attached the work for a,b,c A researcher conducts a study to determine whether spending time outdoors improves happiness. She randomly assigns 42 participants into two groups. One group serves as the control group, while the treatment group is scheduled for outdoor activities 4 days per week. The researcher measures the happiness of each participant and the data reveal the following at the conclusion of her study:- Treatment Group: \( n = 21, M_1 = 8, SS = 9 \)- Control Group: \( n = 21, M_2 = 6, SS = 7 \)What type of design is this study (single-sample, independent measures, repeated measures)?(a) State the null and alternative hypotheses(b) Using an alpha level of 0.05 (\( \alpha = 0.05 \)), identify the critical t-value for this hypothesis test.(c) Compute the standard error for this statistical analysis AND describe what this number tells you specifically for this type of design(d) Compute the t-statistic for this hypothesis test and describe what the t-score tells you(e) Determine whether the outdoor exposure program increased happiness, explaining your decision(f) Compute Cohen’s d and describe what this number tells you in this specific study **Hypotheses:**- \( H_0: M_1 = M_2 \)- \( H_1: M_1 \neq M_2 \)**1. Degree of Freedom:**- Calculated as \( 21 + 21 - 2 = 40 \).**2. Critical Values:**- Alpha level (\( \alpha \)) = 0.05 for a two-tailed test.- Two tails critical value = \( \pm 2.021 \).**3. Pooled Standard Deviation:**- Formula: \[ \sqrt{\frac{(21 - 1)9^2 + (21 - 1)7^2}{21 + 21 - 2}} \]- Calculated as: \[ \sqrt{\frac{20 \times 9^2 + 20 \times 7^2}{40}} = \sqrt{8} = 2.8 \]**4. Standard Error (SE):**- Formula: \[ SE = 2.8 \sqrt{\frac{1}{21} + \frac{1}{21}} \]- Calculation steps: \[ = 2.8 \sqrt{0.0952} = 2.8284 \times 0.3086 \]- Result: \[ = 0.8729 \]**5. Standard Error:**- Final value: \[ = 0.8729 \]This information can be used for concluding statistical significance between two sample means based on the calculated standard error and critical values.

Name: I just need help with d,e,fi attached the work for a,b,c A researcher
Uploaded: 2024-03-05T11:53:49.000Z
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Description: I just need help with d,e,fi attached the work for a,b,c A researcher conducts a study to determine whether spending time outdoors improves happiness. She randomly assigns 42 participants into two groups. One group serves as the control group, while