SOAN 3120 - Homework Assignment #3

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School

University of Guelph *

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3120

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Electrical Engineering

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Feb 20, 2024

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Uploaded by PrivateBoarMaster445

Kyra Dukovac 1191950 SOAN 3120 Instructor R. Broll Homework Assignment #3 Question 1) → Filtered cases to only include those 65 and older USE ALL. COMPUTE filter_$=(dhhgage>=13). VARIABLE LABELS filter_$ 'dhhgage>=13 (FILTER)'. VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'. FORMATS filter_$ (f1.0). FILTER BY filter_$. EXECUTE. → One sample test T-TEST /TESTVAL=150 /MISSING=ANALYSIS /VARIABLES=paadvmva /ES DISPLAY(TRUE) /CRITERIA=CI(.99). One-Sample Statistics N Mean Std. Deviation Std. Error Mean Total minutes of moderate to vigorous activity 214 330.49 407.211 27.820 One-Sample Test Test Value = 150 t df Significance Mean Difference 99% Confidence Interval of the Difference One-Sided p Two-Sided p Lower Upper

Total minutes of moderate to vigorous activity 6.488 213 <.001 <.001 180.486 108.18 252.79 One-Sample Effect Sizes Standardizer a Point Estimate 99% Confidence Interval Lower Upper Total minutes of moderate to vigorous activity Cohen's d 407.211 .443 .258 .627 Hedges' correction 408.650 .442 .257 .625 a. The denominator used in estimating the effect sizes. Cohen's d uses the sample standard deviation. Hedges' correction uses the sample standard deviation, plus a correction factor. Five Step Model: Step 1: Assumptions and Test Requirements: - Model: random sampling ➔ Level of measurement is interval-ratio ➔ Sampling distribution is normal Step 2: State the Null Hypothesis: - 𝐻 0 µ = 150 - 𝐻 0 µ ≠ 150 Step 3: Select the Sampling Distribution and Establish the Critical Region: - Sampling distribution ➔ Alpha = 0.001, two tailed test ➔ df = n - 1 = 214 - 1 = 213 ➔ t critical = 2.358 Step 4. Compute the Test Statistic: - t (critical) = 2.358 - t (obtained) = 6.488 Step 5. Make a Decision and Interpret the Results:

- The obtained t-value resides within the critical region. Consequently, rejecting the null hypothesis implies that individuals aged 65 and over do not engage in or adhere to the recommended 150 minutes of weekly physical activity. Question 2) T-TEST GROUPS=sdcdgcb(1 2) /MISSING=ANALYSIS /VARIABLES=ehg2dvr3 /ES DISPLAY(TRUE) /CRITERIA=CI(.95). Group Statistics Country of birth - grouped N Mean Std. Deviation Std. Error Mean Highest level of education Canada 1275 2.56 .662 .019 Other 455 2.61 .598 .028 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Significance Mean Differen ce Std. Error Differen ce 95% Confidence Interval of the Difference One-Si ded p Two-Si ded p Lower Upper Highest level of education Equal variances assumed 8.859 .003 -1.20 2 1728 .115 .230 -.042 .035 -.112 .027 Equal variances not assumed -1.26 1 878. 421 .104 .208 -.042 .034 -.108 .024 Independent Samples Effect Sizes Standardizer a Point Estimate 95% Confidence Interval Lower Upper Highest level of education Cohen's d .646 -.066 -.173 .041 Hedges' correction .646 -.066 -.173 .041 Glass's delta .598 -.071 -.178 .036

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a. The denominator used in estimating the effect sizes. Cohen's d uses the pooled standard deviation. Hedges' correction uses the pooled standard deviation, plus a correction factor. Glass's delta uses the sample standard deviation of the control (i.e., the second) group. Five-Step Model: Step 1. Assumptions and Test Requirements: - Model is independent random samples - Level of measurement is interval ratio - Population variances are unequal: σ 1 2 ≠ σ 2 2 Step 2. State the Null Hypothesis: Null Hypothesis (H0): There is no significant difference in the likelihood of having a postsecondary certificate, diploma, or university degree between those born outside of Canada and those born in Canada. Alternative Hypothesis (H1): Those born outside of Canada are more likely to have a postsecondary certificate, diploma, or university degree than those born in Canada. Step 3. Select the Sampling Distribution and Establish the Critical Region: - Sample Distribution: T distribution A = 0.05 (confidence interval 95%) two tailed df = (1275-1) (455-1) = (1274) (454) = 1728 t (critical) = 1.980 ± Step 4. Compute the Test Statistic:

- I conducted an independent sample t-test to assess the statistical significance of the difference in education levels between individuals born in Canada and those born outside of Canada. The results indicate non-significance, as the p-value is below 0.05. ➔ T obtained = -1.261 Step 5. Make a Decision and Interpret the Results: ➔ t critical: -1.261 ➔ t obtained: ± 1.980 Given that the obtained t-value does not reside within the critical region, we do not have sufficient evidence to reject the null hypothesis. Therefore, we can infer that individuals born outside of Canada are not statistically more inclined to possess a postsecondary certificate, diploma, or university degree compared to those born in Canada. BONUS: My statistics professor told me I was average … I told him, “That’s MEAN. ” → Also here is a meme that perfectly reflects me.