Free answers to pooled standard deviation problems

Recent questions in Pooled Standard Deviation

Osmarq5ltp 2022-05-09 Answered

Samples are taken from two different types of honey and the viscosity is measured.

Honey A:
Mean: 114.44
S.D : 0.62
Sample Size: 4

Honey B:
Mean: 114.93
S.D: 0.94
Sample Size: 6

Assuming normal distribution, test at 5% significance level whether there is a difference in the viscosity of the two types of honey?

Here's what I did:

I took my null hypothesis as $μ$ B - $μ$ A = 0 and alternative hypothesis as $μ$ B - $μ$ A $\neq$ 0

Then I did my calculations which were as following:

Test Statistic = (B -A ) - ( $μ$ B - $μ$ A) / sqrt {(variance B / sample size B) + (variance A / sample size A)}

This gave me test statistic as = 0.49/0.49332 that is equal to 0.993

However the test statistic in the book solution is given as 0.91. What am I doing wrong?

zuzogiecwu 2022-05-07 Answered

I'm trying to solve following type of combined date given question. Imagined that there's two factories. They are X and Y. "X" factory has 10 workers and "Y" has 20 workers. These two factory's production respectively given as Σx^2=2950 and ΣY^2=5000. Moreover, "X" factory mean is 18 and "Y" factory mean is 15.
If the whole population is considered as a one. How to calculate the mean and standard deviation in a situation like this one? I'm not expecting the final answer, I rather would like to know the procedure that how to solve such a question.