Improve Your Understanding of College Level Statistics Problems

Suppose a researcher conducts a study on the relationship between hours of exercise per week and grade point average at a certain university. To be sure to get an equal number of men and women in the sample, the researcher divides the population into men and women and then randomly selects 200 men and 200 women for the study. What sampling technique did the researcher use?
A. Simple Random Sampling
B. Proportional Stratified Random Sampling
C. Stratified Random Sampling
D. Convenience Sampling

Professor Arig randomly assigned 105 male students who had been referred to the Guidance Center, after a violation of university rules. Students were assigned to undergo (1) Counseling, (2) Gabay, a developed intervention in which students go through series of activities and the material used is related to the students own experiences. Based on inferential statistics, the researches concluded that those in the Counseling group had more violations at follow-up than those in the Gabay group. What is the sampling technique used?
- Simple Random Sampling
- Systematic Sampling
- Startified Random Sampling
- Cluster Random Sampling
- None of the above

What is a 'critical value' in statistics?
The raw material needed for the manufacture of medicine has to be at least $97\mathrm{\%<!--\; \%\; -->}$ pure. A buyer analyzes the nullhypothesis, that the proportion is ${\mathrm{\mu <!--\; \mu \; -->}}_0=97\mathrm{\%<!--\; \%\; -->}$, with the alternative hypothesis that the proportion is higher than $97\mathrm{\%<!--\; \%\; -->}$. He decides to buy the raw material if the nulhypothesis gets rejected with $\mathrm{\alpha <!--\; \alpha \; -->}=0.05$. So if the calculated critical value is equal to $t_{\mathrm{\alpha <!--\; \alpha \; -->}}=98\mathrm{\%<!--\; \%\; -->}$, he'll only buy if he finds a proportion of $98\mathrm{\%<!--\; \%\; -->}$ or higher with his analysis. The risk that he buys a raw material with a proportion of $97\mathrm{\%<!--\; \%\; -->}$ (nullhypothesis is true) is $100\times <!--\; \times \; -->\mathrm{\alpha <!--\; \alpha \; -->}=5\mathrm{\%<!--\; \%\; -->}$

$X_i\sim <!--\; \sim \; -->Bern(p)$, $Y=\underset{i=1}{\overset{N}{\sum <!--\; \sum \; -->}}{X}_i$ and $H_0:p\ge <!--\; \ge \; -->0.5$ vs $H_1:p<0.5$ with $\mathrm{\alpha <!--\; \alpha \; -->}=0.05$.
I have to find the $p$-value at $n=30$ and $y=5$.
I'm not sure if this correct, but I figured the $p$-value was simply:
$P(Y\le <!--\; \le \; -->5)=\underset{i=1}{\overset{5}{\sum <!--\; \sum \; -->}}(\genfrac{}{}{0ex}{}{30}{y})(0.5{)}^y(0.5{)}^{30-<!--\; -\; -->y}$
which works out to be $0.00016$.
If this is correct, then why have I been given $\mathrm{\alpha <!--\; \alpha \; -->}$?

Summarize the four types of a hypothesis test. Be sure to include any formula and important tips and terminology.
1. Hypothesis
2. Model:
3. Mechanics:
4. Conclusion:

Which of the following is / are TRUE about risk analysis? Choose all that apply.
$\mathrm{◻<!--\; ◻\; -->}$ Risk analysis involves a detailed consideration of the uncertainties
$\mathrm{◻<!--\; ◻\; -->}$ Purpose of analysis may influence the detail and complexity of risk analysis
$\mathrm{◻<!--\; ◻\; -->}$ Risk analysis involves a detailed consideration of controls
$\mathrm{◻<!--\; ◻\; -->}$ Availability of information may influence the detail and complexity of risk analysis

Determine the type of sampling used to collect data In a medical research studya researcher selects hospital and interviews the patients that day Please select the correct answer below Random sampling Systematic Sampling Stratified Sampling Cluster Sampling

What is a numerical variable and what is a categorical variable?

What is the importance of descriptive statistics?

If you were given a choice to conduct a quantitative risk analysis or a qualitative risk analysis, which option would you choose and why? How would you go about completing the risk analysis?

What will happen to the median of a data set if you add a positive number to every value?

Suppose we are testing 20 drugs and use a significance value of 0.01 in each test. Suppose at least one out of the 20 tests rejects the null hypothesis. What is the upper bound for the probability that declaring the corresponding drug useful is a type I error (i.e. reject null hypothesis when one should not)?
I am confused on where to start. Any help is appreciated

How do you find the mean of data set 10, 0, 2, and 8?

According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too low. To investigate, the analyst selects a random sample of 500 households and finds that 98% of them purchase toilet paper. We found that we do not have convincing evidence at the α = 0.05 level to conclude that the true proportion of all households that purchase toilet paper differs from 0.97.
The power of this test to reject p = 0.97 if 0.98 is true is 0.21. If the analyst were to decrease the significance level of the test, how would the power be affected?
It would increase.
It would decrease.
It would remain the same.
It would double.

What is the average of 32, 48, 60, 74?

Is the sample standard deviation "s" a resistant measure?

The mean age of 6 women in an office is 31 years old. The mean age of 4 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office?

Which of the following will assess key political refulations susceptible to affect business condcted in a specific country?
$\circ <!--\; \circ \; -->$ Multidimensional political risk analysis
$\circ <!--\; \circ \; -->$ Micro political analysis
$\circ <!--\; \circ \; -->$ Macro political analysis
$\circ <!--\; \circ \; -->$ Standard political analysis

Does accelerating cosmological expansion increase beam spread?
In the standard textbook case, a transmitter of diameter $D$ can produce an electromagnetic beam of wavelength $\mathrm{\lambda <!--\; \lambda \; -->}$ that has spread angle $\mathrm{\theta <!--\; \theta \; -->}=1.22\mathrm{\lambda <!--\; \lambda \; -->}/D$. But what happens in an expanding cosmology, especially one that accelerates so that there is an event horizon? Does $\mathrm{\theta <!--\; \theta \; -->}$ increase with distance?
Obviously each photon will travel along a null geodesic and after conformal time $\mathrm{\tau <!--\; \tau \; -->}$ have travelled $\mathrm{\chi <!--\; \chi \; -->}=c\mathrm{\tau <!--\; \tau \; -->}$ units of co-moving distance. The distance between the beam edges would in flat space be growing as $\mathrm{\delta <!--\; \delta \; -->}=2c\sin <!--\; \; -->(\mathrm{\theta <!--\; \theta \; -->}/2)\mathrm{\tau <!--\; \tau \; -->}$. Now, co-moving coordinates are nice and behave well with conformal time, so I would be mildly confident that this distance is true as measured in co-moving coordinates.
But that means that in proper distance the beam diameter is multiplied by the scale factor, $a(t)\mathrm{\delta <!--\; \delta \; -->}$ (where $t$ is the time corresponding to $\mathrm{\tau <!--\; \tau \; -->}$), and hence $\mathrm{\theta <!--\; \theta \; -->}$ increases. However, the distance to the origin in these coordinates has also increased to $a(t)(ct)$, so that seems to cancel the expansion - if we measure $\mathrm{\theta <!--\; \theta \; -->}(t)$ globally by dividing the lengths.
But it seems that locally we should see the edges getting separated at an accelerating pace; after all, the local observers will see the emitter accelerating away from them, producing a wider and wider beam near their location since it was emitted further away. From this perspective as time goes by the beam ends up closer and closer to $\mathrm{\theta <!--\; \theta \; -->}=\mathrm{\pi <!--\; \pi \; -->}$ (and ever more red-shifted, which presumably keeps the total power across it constant).
Does this analysis work, or did I slip on one or more coordinate systems?