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What is the mathematical formula for the pooled variance of two populations?

Twenty volunteers at a cold research institute caught a cold after having been exposed to various cold viruses. Ten of the volunteers were randomly selected to receive tablets containing 1 gram of vitamin C. These tablets were taken four times a day. The control group, consisting of the other 10 volunteers, was given placebo tablets that looked and tasted exactly like the vitamin C ones. This was continued for each volunteer until a doctor, who did not know whether one volunteer was receiving vitamin C or the placebo, decided that the volunteer was no longer suffering from the cold. The length of time the cold lasted was then recorded. At the end of the experiment, the following data resulted
:The average length of cold for the $n_1=$=10 people treated with vitamin C is with a standard deviation of $s_1=$=0.76
The average length of cold for the $n_2=$=10 people receiving the placebo is with a standard deviation of $s_2=$0.85
Determine the value of the pooled standard deviation . Round your answer three decimal places.

What is a pooled variance?

In order to test the difference in populations means, samples were collected for two independent populations where the variances are assumed unknown and equal and the population normally distributed. The following data resulted:
Sample 1 -
$x_1=112,s_1=14,n_1=25$
Sample 2 -
$x_2=107,s_2=17,n_2=28$

The value of the pooled standard deviation is approximately 15.66. True or False?

How do you find the pooled standard deviation in an ANOVA table?

can you write out this formula in the form of a sentence ?
$ES=\frac{\stackrel{¯<!--\; ¯\; -->}{X_1}-<!--\; -\; -->\stackrel{¯<!--\; ¯\; -->}{X_2}}{s}$

The denominator of the t score formula for the independent-samples t-test is ______.

1 - population standard error
2 - estimated pooled standard deviation
3 - estimated pooled variance
4 - estimated standard error

Find the pooled estimate of the standard deviation if n1 = 18, n2 = 14, S1= 3.3, and S2= 2.5.
(Write two decimal places)

How are the variance and the standard deviation of a distribution related? What is measublack by the standard deviation?

Which is greater: the sample standard deviation or the population standard deviation? Explain.

True or False? Assume a researcher recruits 150 African American and Caucasian individuals taking warfarin to determine if there is a difference in the mean dosage of the medication. If the mean dosage for 75 Caucasian individuals requiblack to get their INR blood test in range is 6.1 mg with a standard deviation of 1.7 mg and the mean dosage for 75 African American individuals requiblack to get their INR blood test in range is 4.3 mg with a standard deviation of 0.9 mg, the decision rule for a 10% level of significance would be to reject H0 if z $\le <!--\; \le \; -->$ -1.645 or z $\ge <!--\; \ge \; -->$ 1.645

How are two-sample t-tests different from two sample z-tests?

What is pooled standard deviation and how is it calculated ?

Consider the data with analysis shown in the following computer output:
$\begin{array}{|cccc|}\hline \text{ Level }& \text{ N }& \text{ Mean }& \text{ StDev }\\ \text{ A }& 4& 10.500& 2.902\\ \text{ B }& 5& 16.800& 2.168\\ \text{ C }& 6& 10.800& 2.387\\ \hline\end{array}$
$\begin{array}{|cccccc|}\hline \text{ Source }& \text{ DF }& \text{ SS }& \text{ MS }& \text{ F }& \text{ P }\\ \text{ Groups }& 2& 125.07& 62.54& 10.34& 0.002\\ \text{ Error }& 12& 72.55& 6.05\\ \text{ Total }& 14& 197.62\\ \hline\end{array}$
What is the pooled standard deviation? What degrees of freedom are used in doing inferences for these means and differences in means?

Round your answer for the pooled standard deviation to two decimal places.

The pooled standard deviation is =
degrees of freedom =

A two sample (independent-sample) study with n = 6 in each sample, produces a sample mean difference of 4 points and a pooled variance of 12. What is the value for the sample t score?Group of answer choices
A)1
B)2
C)4/6
D)4/8

Comparison between two diets in obese children, one low-fat and one low-carb 8 week intervention with the outcome of weight loss. Based on a similar study in adults, 20% of the children will not complete the study. For a 95% confidence interval with a margin of error of no more than 3 lbs., how many children should be recruited? In the adult trial, the low-fat and low-carb groups had a standard deviations of 8.4 and 7.7, respectively and each group had 100 participants.
A. Calculate the pooled standard deviation (Sp).
B. Calculate the number of children will need to be recruited for the trial if all finish the study use the Sp calculated for the standard deviation?
C. How many children would be needed to account for 20% attrition.

Explain in your own words what pooled variance is. If you have two different samples of different sizes (the n for each group is different_, explain wether the value of the pooled variance will be closer to the larger sample or smaller sample.

The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. Use alpha = 0.01. What is the pooled standard deviation?

How would actuarial science refer to the idea that the premium should increase as number of insured entities decreases.
In other words, what is the technical term for the intuition that I would charge a higher premium per car to insure just one car than to insure 1000 cars, if such intuition is even justified.
As a sketch of my thinking on this, I have defined risk-adjusted premium as the total premium to cover losses divided by the standard deviation of the total loss on the portfolio of policies. I believe both the numerator and the denominator can be deduced from the law of large numbers.

I have the following data on duration that different aged adults can remain standing.
$\begin{array}{|cccc|}\hline \text{ Age }& \text{ Sample Size }& \text{ Sample Mean }& \text{ Sample Std Dev }\\ \text{ Old }& 28& 801& 117\\ \text{ Young }& 16& 780& 72\\ \hline\end{array}$
The data I'm using has a normal distribution with the same variances. I want to do a test of hypotheses however at a significance level of 5% (a=0.05) to be able to confirm whether or not the average duration that older adults can remain standing is larger than among younger adults.

I'm not sure which of the different formulas I should use however to determine this due to my sample size being relatively small. Should I be using the following test.

to compute pooled standard deviation: $s^2=\frac{(1-<!--\; -\; -->1)s{1}^2+(n2-<!--\; -\; -->1)s{2}^2}{n1+n2-<!--\; -\; -->2}$

compute test statistics: $t=\frac{y1-<!--\; -\; -->y2-<!--\; -\; -->0}{s\sqrt{\frac{1}{n1}+\frac{1}{n2}}}$