Improve Your Understanding of College Level Statistics Problems

Question about t statistic. Of these two, which formula is correct?
$t(x)=\frac{\stackrel{¯<!--\; ¯\; -->}{X}-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->}}{\sqrt{\frac{1}{n}\sum <!--\; \sum \; -->{(X_i-<!--\; -\; -->\stackrel{¯<!--\; ¯\; -->}{X})}^2}}\sqrt{n-<!--\; -\; -->1}$
$t(x)=\frac{\stackrel{¯<!--\; ¯\; -->}{X}-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->}}{\sqrt{\frac{1}{n-<!--\; -\; -->1}\sum <!--\; \sum \; -->{(X_i-<!--\; -\; -->\stackrel{¯<!--\; ¯\; -->}{X})}^2}}\sqrt{n}$

A district in the Ashanti region town has 102 towns and villages. If you interviewed everyone living in one village, would you be interviewing a population or a sample from the village?

How To Calculate Standard Deviation??

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.

What conditions must be met for conducting a two-sample t test for the means?

How do you find the exact value of $\sin <!--\; \; -->(\frac{x}{2})$ and $\cos <!--\; \; -->(\frac{x}{2})$ if $\cos <!--\; \; -->x=-<!--\; -\; -->\frac{1}{4}$ and $\mathrm{\pi <!--\; \pi \; -->}<x<2\mathrm{\pi <!--\; \pi \; -->}$?

Why does the margin of error decrease as the sample size n increases?

Data from a sample survey contain 28% foreign born and 72% native born when the population of interest is 22-78. What procedure adjusts the sample to match the population?
A. Standardization
B. Averaging
C. Weighting

How can convenience samples be biased?

For each of the following measures, give the value that implies no difference between the two groups being compared. Relative risk. Odds ratio. Percent increase in risk.

A local high school counselor is interested in studying how teacher perceptions of students, as being intelligent or not, affect the success of freshman students in the classroom. The school creates an Excel spreadsheet listed all the freshman students in alphabetical order and places their names into one of two columns. All students listed in the second column are selected to participate in this study. Is this design an example of random sampling? Explain. Show work

The concentration of alcohol in a person's bloodstream is measurable. Suppose that the relative risk R of having an accident while driving a car can be modeled by an equation of the form $R=e^{kx}$ where x is the percent of concentration of alcohol in the bloodstream andk is a constant. Suppose that a concentration of alcohol in the bloodstream of 0.03 percent results in a relative risk of an accident of 1.4. Find the constant k in the equation.

Suppose $X_1,\dots <!--\; \dots \; -->,X_m$ and $Y_1,\dots <!--\; \dots \; -->,Y_n$ are random variables with the property that $Cov(X_i,Y_j)<\mathrm{\infty <!--\; \infty \; -->}$ for all i and j. Show that, for any constants $a_1,\dots <!--\; \dots \; -->,a_m$ and $b_1,\dots <!--\; \dots \; -->,b_n$,
$Cov(\underset{i=1}{\overset{m}{\sum <!--\; \sum \; -->}}{a}_i{X}_i,\underset{j=1}{\overset{n}{\sum <!--\; \sum \; -->}}{b}_j{Y}_j)=\underset{i=1}{\overset{m}{\sum <!--\; \sum \; -->}}\underset{j=1}{\overset{n}{\sum <!--\; \sum \; -->}}{a}_i{b}_{j}Cov(X_i,Y_j)$

True and False?
If the product $A\times <!--\; \times \; -->B$ of two sets $A$ and $B$ is the empty set , then both $A$ and $B$ have to be empty set.

What is Cluster sampling and Explain with an example of research which uses cluster sampling.

How do you find the exact value of $\sin <!--\; \; -->({\sin }^{-<!--\; -\; -->1}<!--\; \; -->(0.3))$?