Inferantial statistic presentation about two sample t test

Inferantial statistic presentation about two sample t test

1. Two Sample T test Prepared by: Salman And Muhammad Talha Teacher Name: Amad Khalil Subject: Inferential Statistics

2. Outlines T-test Types Advantages of two sample T-test Disadvantages of Two sample T-Test Example Hypothesis Testing Conclusion

3. T-Test: A t-test is a statistical method used to determine if there is a significant difference between the means of two groups. One-Sample T-Test: Used when comparing the mean of a sample to a known value or hypothesized population mean. For example, you might use a one-sample t-test to determine if the average height of a group of individuals is significantly different from a known average height. Two-Sample T-Test: Used when comparing the means of two independent groups. For instance, in a clinical trial, you might use a two-sample t-test to determine if there is a significant difference in the effectiveness of a new drug compared to a placebo.

4. Advantages of Two-Sample T-Test: Simplicity: The two-sample t-test is relatively straightforward and easy to understand, making it accessible to a wide range of researchers and analysts. Small Sample Sizes: It can be effective even with small sample sizes, provided the data is approximately normally distributed.

5. Disadvantages of Two-Sample T-Test: Equal Variances: The standard t-test assumes equal variances between the two groups. If variances are significantly different, alternative versions of the test (such as the Welch's t-test) may be more appropriate. Non-Normal Data: The two-sample t-test is less accurate when dealing with strongly non-normal data, especially if sample sizes are small.

6. Formula = =  

7. Year Inflation Rate (Pakistan) Inflation Rate (Bangladesh) 2008 12.0 8.9 2009 19.6 7.6 2010 10.1 6.8 2011 13.7 10.9 2012 11 8.9 2013 7.4 6.8 2014 8.6 7.3 2015 4.5 6.4 2016 2.9 5.9 2017 4.1 5.4 2018 3.9 5.8 2019 6.7 5.5 2020 10.7 5.6 2021 8.9 5.6 2022 12.1 6 2023 29.2 6.2

8. Question Is there a significant difference in the mean inflation rates between Pakistan and Bangladesh for the years 2008 to 2023? Perform a two-sample t-test to compare the inflation rates of both countries, with the null hypothesis stating no significant difference and the alternative hypothesis suggesting otherwise. Use a significance level of 0.05.

9. Year Inflation Rate (Pakistan) (X) Inflation Rate (Bangladesh) (Y) X-Y(d) d - d (d – d) 2 2008 12.0 8.9 3.1 -0.3875 0.150 2009 19.6 7.6 12 8.5125 72.463 2010 10.1 6.8 3.3 -0.1875 0.035 2011 13.7 10.9 2.8 -0.6875 0.472 2012 11 8.9 2.1 -1.3875 1.925 2013 7.4 6.8 0.6 -2.8875 8.337 2014 8.6 7.3 1.3 -2.1875 4.785 2015 4.5 6.4 -1.9 -5.3875 29.025 2016 2.9 5.9 -3 -6.4875 42.087 2017 4.1 5.4 -1.3 -4.7875 22.920 2018 3.9 5.8 -1.9 -5.3875 29.025 2019 6.7 5.5 1.2 -2.2875 5.232 2020 10.7 5.6 5.1 1.6125 2.6 2021 8.9 5.6 3.3 -0.1875 0.035 2022 12.1 6 6.1 2.6125 6.825 2023 29.2 6.2 23 19.5125 380.737 ∑d=55.8 d = 55.8/16=3.4875 ∑(d – d ) 2 = 606.658

10. Step 1 H o : μ 1 = μ 2 H A : μ 1 ≠ μ 2 Step 2 = = = 6.359 = = = = = 2.1937  

11. Step 3 df = 16-1 = 15 Step 4 T (15) (0.05) = ± 2.131

12. Conclusion After conducting a two-sample t-test with a significance level of 0.05 to compare the mean inflation rates between Pakistan and Bangladesh for the years 2008 to 2023, we reject the null hypothesis. There is sufficient evidence to conclude that there is a significant difference in the mean inflation rates between the two countries during this period. Source https://en.wikipedia.org/wiki/Economy_of_Pakistan https://en.wikipedia.org/wiki/Economy_of_Bangladesh