Can you conclude that there is a real difference between X and Y? Use the approp

Question

Can you conclude that there is a real difference between X and Y? Use the appropriate hypothesis test. Use an alpha of 0.05. Be sure to clearly state the null and alternative hypotheses.

X 15.99365 15.51946 15.71114 14.77224 14.67946 15.0832 14.39106 10.80908 13.86464 13.05463 15.50061 13.7629 18.03905 15.79939 10.34195 12.25423 15.12416 21.39559 13.74588 16.92596 9.518676 11.85892 15.89073 10.78407 19.56801 12.02397 14.75108 17.10459 14.3025 15.93867 12.20338 10.22933 13.99488 17.26279 14.65768 15.83615 20.29761 9.357604 12.65152 14.82175 20.48137 15.58844 12.12441 12.18624 18.77543 15.63177 11.93871 11.48123 10.5021 16.76238 12.58015 19.35946 18.34315 16.65182 Y 16.11383 12.21679 12.54831 11.77001 9.905113 10.55479 10.1213 12.29959 14.47059 11.0882 6.596125 11.40695 10.49983 12.5921 15.93683 16.71548 13.93784 14.11894 14.88866 11.43744 6.885664 5.838637 11.51013 11.76756 7.786938 7.31743 10.16603 13.36175 16.61404 9.413675 11.33574 11.10582 10.67266 12.85222 12.4092 11.16221 8.853602 15.14525 11.15134 13.58139 8.657948 12.66292 9.662953 15.0578 12.27691 7.371203 6.876354 9.073733 11.62291 13.56349 12.85249 14.86432 14.68897 16.51115

Explanation / Answer

H0:  1 =  2

HA: 1 !=  2

Similarly for Y, we have-

1^2/n1 + 2^2/n2 = 0.154 + 0.139 = 0.293

k=Sqrt(0.293) = 0.541

Z-Stat = [(x1-x2)-(1-2)]/k = 2.97/0.541 = 5.489

P-value is in the range of 0.01 for this z

P<alpha

Reject H0

So, we cannot say X and Y are same

Hope this helps and Please don't forget to rate the answer :)

n1 54 x1 14.7 1 2.89

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