To calculate the paired sample t-test, we first need to calculate the differences between the two variables (seconds and speed). Then, we can proceed with the t-test calculation.
Let's calculate the differences:
Seconds difference = (144 - 37.5) = 106.5
Seconds difference = (149.2 - 36.193029) = 113.006971
Seconds difference = (148.2 - 36.437247) = 111.762753
Seconds difference = (149 - 36.241611) = 112.758389
Seconds difference = (149.6 - 36.096257) = 113.503743
Seconds difference = (146.8 - 36.784741) = 110.015259
Seconds difference = (148.6 - 36.339166) = 112.260834
Seconds difference = (149.8 - 36.048064) = 113.751936
Seconds difference = (149 - 36.241611) = 112.758389
Seconds difference = (148.2 - 36.437247) = 111.762753
Now, let's calculate the mean of the differences and the standard deviation:
Mean of differences (Mdiff) = (106.5 + 113.006971 + 111.762753 + 112.758389 + 113.503743 + 110.015259 + 112.260834 + 113.751936 + 112.758389 + 111.762753)/10 = 111.3930243
Standard deviation (s) of the differences = sqrt(((106.5 - 111.3930243)^2 + (113.006971 - 111.3930243)^2 + ... + (111.762753 - 111.3930243)^2)/9) = 1.989624995
Next, let's calculate the t-test statistic:
t = (Mdiff - µdiff) / (s / sqrt(n))
Where,
µdiff = 0 (null hypothesis: no difference between the mean seconds and speed)
n = 10 (number of paired measurements)
t = (111.3930243 - 0) / (1.989624995 / sqrt(10)) = 21.90220996
Finally, we need to compare the calculated t-value with the critical t-value at alpha level 0.05. Since we don't have the degrees of freedom or the exact table value, we can use statistical software or online calculators to find the critical t-value. If the calculated t-value is greater than the critical t-value, we can reject the null hypothesis.
Please note that this is a general calculation process and actual t-value or software result may vary.
The student conduct data for seconds and speed. She found the following, seconds
144,149.2,148.2,149,149.6,146.8,148.6,149.8,149,148.2 and for speed 37.5,36.193029,36.437247,36.241611,36.096257,36.784741,36.339166,36.048064,36.241611,36.437247.Calculate paired sample t test for . Using alpha 0.05.
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