5. Two-tailed hypothesis testing - Step by step dfProportion in One Tail0.250.100.050.0250.010.005Proportion in Two Tails Combined0.500.200.100.050.020.0111.0003.0786.31412.70631.82163.65720.8161.8862.9204.3036.9659.92530.7651.6382.3533.1824.5415.84140.7411.5332.1322.7763.7474.60450.7271.4762.0152.5713.3654.03260.7181.4401.9432.4473.1433.70770.7111.4151.8952.3652.9983.49980.7061.3971.8602.3062.8963.35590.7031.3831.8332.2622.8213.250100.7001.3721.8122.2282.7643.169110.6971.3631.7962.2012.7183.106120.6951.3561.7822.1792.6813.055130.6941.3501.7712.1602.6503.012140.6921.3451.7612.1452.6242.977150.6911.3411.7532.1312.6022.947160.6901.3371.7462.1202.5832.921170.6891.3331.7402.1102.5672.898180.6881.3301.7342.1012.5522.878190.6881.3281.7292.0932.5392.861200.6871.3251.7252.0862.5282.845210.6861.3231.7212.0802.5182.831220.6861.3211.7172.0742.5082.819230.6851.3191.7142.0692.5002.807240.6851.3181.7112.0642.4922.797250.6841.3161.7082.0602.4852.787260.6841.3151.7062.0562.4792.779270.6841.3141.7032.0522.4732.771280.6831.3131.7012.0482.4672.763290.6831.3111.6992.0452.4622.756300.6831.3101.6972.0422.4572.750400.6811.3031.6842.0212.4232.704600.6791.2961.6712.0002.3902.6601200.6771.2891.6581.9802.3582.617∞0.6741.2821.6451.9602.3262.576 **Educational Content: Understanding Hypothesis Testing**In this exercise, we focus on the key components involved in hypothesis testing, particularly when working with the t-distribution.1. **Critical t scores**: The values that define the borders of the critical region are essential for determining whether to reject the null hypothesis. 2. **Estimated Standard Error**: This value quantifies the dispersion of the sample mean distribution and is necessary to calculate the t-statistic.3. **T Statistic**: This is the calculated value used to determine whether the test statistic falls within the critical region.4. **Hypothesis Testing Conclusion**: - If the t statistic falls in the critical region, the decision is to reject the null hypothesis. - The researcher's conclusion is that SAM-e (S-adenosylmethionine) has a significant effect on the moods of cancer patients. These elements are connected and essential for analyzing the data and drawing conclusions in the context of statistical hypothesis testing. **SAM-e and Depression Study****Introduction:**S-adenosyl methionine (SAM-e) is a naturally occurring compound in human cells, believed to impact depression symptoms. A researcher is investigating the effects of SAM-e on cancer patients experiencing depression. A sample of \( n = 30 \) patients is asked to take a suggested dosage daily for four weeks. After this period, each participant takes the Beck Depression Inventory (BDI), a 21-item self-report tool for assessing depression severity.**Study Details:**- **Sample Mean (M):** 28.9- **Standard Deviation (s):** 5.94- **Population Test Mean (μ):** 29.7With no prior studies on SAM-e's impact on this group, a two-tailed single-sample t-test is utilized to explore effects.**Hypotheses Selection:**Choose the correct null (H₀) and alternative (H₁) hypotheses for this study:- \( \circ \) **Option 1:** \( H₀: \mu_{\text{SAM-e}} \neq 29.7; \, H₁: \mu_{\text{SAM-e}} = 29.7 \)- \( \circ \) **Option 2:** \( H₀: \mu_{\text{SAM-e}} \geq 29.7; \, H₁: \mu_{\text{SAM-e}} < 29.7 \)- \( \circ \) **Option 3:** \( H₀: \mu_{\text{SAM-e}} = 29.7; \, H₁: \mu_{\text{SAM-e}} \neq 29.7 \)- \( \circ \) **Option 4:** \( H₀: \mu_{\text{SAM-e}} \geq 29.7; \, H₁: \mu_{\text{SAM-e}} > 29.7 \)**Assumptions and Calculations:**Assume that depression scores are normally distributed in patients using SAM-e. Determine the degrees of freedom (ddf).Degrees of freedom (df) = \( n - 1 = 30 - 1 \).**Finding the Critical Region:**Use the t-distribution table to find the critical region for \( \alpha = 0.05 \).This framework provides guidance

Given that Sample size n = 30 Sample mean = 28.9 Sample SD = 5.94 Level of significance = 0.05

Answered: The critical t scores (the values that…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

df	Proportion in One Tail
0.25	0.10	0.05	0.025	0.01	0.005
Proportion in Two Tails Combined
0.50	0.20	0.10	0.05	0.02	0.01
1	1.000	3.078	6.314	12.706	31.821	63.657
2	0.816	1.886	2.920	4.303	6.965	9.925
3	0.765	1.638	2.353	3.182	4.541	5.841
4	0.741	1.533	2.132	2.776	3.747	4.604
5	0.727	1.476	2.015	2.571	3.365	4.032
6	0.718	1.440	1.943	2.447	3.143	3.707
7	0.711	1.415	1.895	2.365	2.998	3.499
8	0.706	1.397	1.860	2.306	2.896	3.355
9	0.703	1.383	1.833	2.262	2.821	3.250
10	0.700	1.372	1.812	2.228	2.764	3.169
11	0.697	1.363	1.796	2.201	2.718	3.106
12	0.695	1.356	1.782	2.179	2.681	3.055
13	0.694	1.350	1.771	2.160	2.650	3.012
14	0.692	1.345	1.761	2.145	2.624	2.977
15	0.691	1.341	1.753	2.131	2.602	2.947
16	0.690	1.337	1.746	2.120	2.583	2.921
17	0.689	1.333	1.740	2.110	2.567	2.898
18	0.688	1.330	1.734	2.101	2.552	2.878
19	0.688	1.328	1.729	2.093	2.539	2.861
20	0.687	1.325	1.725	2.086	2.528	2.845
21	0.686	1.323	1.721	2.080	2.518	2.831
22	0.686	1.321	1.717	2.074	2.508	2.819
23	0.685	1.319	1.714	2.069	2.500	2.807
24	0.685	1.318	1.711	2.064	2.492	2.797
25	0.684	1.316	1.708	2.060	2.485	2.787
26	0.684	1.315	1.706	2.056	2.479	2.779
27	0.684	1.314	1.703	2.052	2.473	2.771
28	0.683	1.313	1.701	2.048	2.467	2.763
29	0.683	1.311	1.699	2.045	2.462	2.756
30	0.683	1.310	1.697	2.042	2.457	2.750
40	0.681	1.303	1.684	2.021	2.423	2.704
60	0.679	1.296	1.671	2.000	2.390	2.660
120	0.677	1.289	1.658	1.980	2.358	2.617
∞	0.674	1.282	1.645	1.960	2.326	2.576