The average number of articles produced by two machines per day are 145 and 120 with standard deviation $S=20.$ On the basis of 18 day production, a standard calculated t-statistics from this given data as 4.2 but it is incorrect. The correct t-statistics is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3.75
To give the t-statistics,
$t=\frac{\bar{x_1}-\bar{x_2}}{s_p\sqrt{\frac{2}{n}}}$
$s_p\sqrt{\frac{2}{n}}=20×\sqrt{\frac{2}{18}}=\frac{20}{3}≃6.67$
$t=\frac{145-120}{6.67}=3.75$