Give a full and correct answer for thew given queston In a causal-analysis with group 1 and group 2, (a) we want to compare the population proportion

Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?

In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference

Give a full and correct answer what is inference concerning the ration of two populations?

Give a correct answer for the difference between internal and external validity is best described as:

To explain: why the combination $(\genfrac{}{}{0ex}{}{n}{r})=(\genfrac{}{}{0ex}{}{n}{r,n-r})$

Indicate true or false for the following statements. If false, specify what change will make the statement true.
a) In the two-sample t test, the number of degrees of freedom for the test statistic increases as sample sizes increase.
b) When the means of two independent samples are used to to compare two population means, we are dealing with dependent (paired) samples.
c) The ${\displaystyle x^2}$ distribution is used for making inferences about two population variances.
d) The standard normal (z) score may be used for inferences concerning population proportions.
e) The F distribution is symmetric and has a mean of 0.
f) The pooled variance estimate is used when comparing means of two populations using independent samples.
g) It is not necessary to have equal sample sizes for the paired t test.

Your friend brags about his ability to do pull-ups. To demonstrate his skills, he has calculated the average number of pull-ups he can do. He wants to know if this significantly exceed the average pull-ups men in the United States can do. The average pull-ups for men in the United States is 8 reps.
A). z-test or t-test, and why?
B). What are the H1 and H0?