Improve Your Understanding of College Level Statistics Problems

What is the mode of this set of data: 10 11 12 12 15 19 20 21 22?

What is the rule of 1.96 for estimating confidence intervals?

What sample size is necessary for 95% CI?
A state legislator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions.
a. What sample size is necessary if the 95% CI for p is to have a width of at most 0.10 irrespective of p?
b. If the legislator has strong reason to believe that at least ${\displaystyle \frac{2}{3}}$ of the electorate know of her position, how large a sample size would you recommend?

What statistic would you use if you had one independent variable ‘geographic location’ (North, South, East, West), and one dependent variable ‘satisfaction with living environment’ (Yes, No)? Explain why.

Which chi-square test should be used on the following study?
A psychotherapist wanted to see what percentages that patients sought after four different kinds of therapy consisting of play, dance, music and group therapy.
a.goodness of fit
b.test of independence

Which of the following statement is FALSE about the Chi-square test?
a. Chi-square test assumes one non-random sample is drawn from an independent population.
b. Chi-square test is used to compare observed frequencies in several categories corresponding with expected frequencies.
c. If more than 20% of the expected frequencies are less than 5, the Chi-square test is not recommended.
d. The data in a contingency table must be in the form of counts for the Chi-square to be valid.

Which would be the appropriate way to test differences in proportions for more than two samples?
a. t-test if variance is unknown
b. z-test
c. paired t-test
d. F-test for equality of variances
e. cross-tabulation procedure to conduct a chi-square test

Which of the statements are correct?
1 .A condition for using the chi-square goodness-of-fit test is that all expected counts must be at least five.
2. The chi-square goodness-of-fit test uses 1 - n degrees of freedom.
3. A condition for using the chi-square goodness-of-fit test is the observations are based on a random sample.
a. I only
b. II only
c. I and III only
d. II and III only
e. I, II, and III

What is the radius of a "Gaussian" sphere such that approx. all the population lie within?
Let ${\displaystyle \mathbf{X}\in B{\mathbf{R}}^n}$ be a random vector distributed normally, i.e. ${\displaystyle \mathbf{X}\sim \mathcal{N}(\mathbf{0},{\sigma }^2{I}_n)}$, where ${\displaystyle \sigma >0}$ is the standard deviation and ${\displaystyle I_n}$ is the identity matrix of order n.SNKIn the case of the univariate Gaussian distribution, i.e.,
${\displaystyle X\sim N(0,{\sigma }^2)}$, we say that approximately 99.7% of the population lie within three standard deviations.
What would be an appropriate constant in the case of the multivariate "isotropic" Gaussian distribution, i.e., ${\displaystyle \mathbf{X}\sim \mathcal{N}(\mathbf{0},{\sigma }^2{I}_n)}$? That is, what would be the radius of the n-sphere in terms of the standard deviation ${\displaystyle \sigma }$, such that approximately all the population lie within?
P.s.: Please feel free to edit the title (and/or the body of this question). I was not sure how to express what I wanted in the title.

When conducting a chi-square test of independence in a contingency table, as the difference between observed frequency and expected frequency ____, the probability of rejecting the null hypothesis increases.
a) stays the same
b) decreases
c) increases
d) goes to 0

When blocking is used, discuss how the blocks are likely to be selected and whether their selection method has an impact on the analysis of variance procedure.

When we carry out a chi-square goodness-of-fit test for a normal distribution, the null hypothesis states that the population?

When to use a chi- square test?

Which of the following is an assumption required by the chi-square test?
a. small samples
b. the frequencies in each cell are relatively similar
c. the sample was randomly selected
d. the variables are normally distributed

Which test? For each of the following situations, statewhether you’d use a chi-square goodness-of-fit test,a chi-square test of homogeneity, a chi-square test ofindependence, or some other statistical test:
a) A brokerage firm wants to see whether the type ofaccount a customer has (Silver, Gold, or Platinum)affects the type of trades that customer makes (in per-son, by phone, or on the Internet). It collects a randomsample of trades made for its customers over the pastyear and performs a test.
b) That brokerage firm also wants to know if the type ofaccount affects the size of the account (in dollars). Itperforms a test to see if the mean size of the account isthe same for the three account types.
c) The academic research office at a large communitycollege wants to see whether the distribution ofcourses chosen (Humanities, Social Science, orScience) is different for its residential and nonresi-dential students. It assembles last semester’s data andperforms a test.

(b) Suppose that, on average, the number of car accidents in Hong Kong are 6 per day (which has 24 hours).i. Determine the probability that at least x accidents will occur in 12 hour period. (4 marks) ii. In a two days, if there were 8 car accidents in Hong Kong, what is the probability that 2 accidents have occurred in the first 12 hours of the two days?

Sex of studenet is qualitative or quantitative

You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: ${\displaystyle H_0}$: pA=0.3,pB=0.1; pC=0.1; pD=0.5
Complete the table. Report all answers accurate to three decimal places.
$\begin{array}{|ccc|}\hline \text{ Category }& \text{ Observed Frequency }& \text{ Expected Frequency }\\ \text{ A }& 24\\ \text{ B }& 12\\ \text{ C }& 7\\ \text{ D }& 44\\ \hline\end{array}$
What is the chi-square test-statistic for this data?
${\displaystyle {\chi }^2=}$
What is the P-Value?
P-Value=

You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.
$\begin{array}{|ccc|}\hline \text{ Category }& \text{ Population \#1 }& \text{ Population \#2 }\\ \text{ A }& 11& 14\\ \text{ B }& 56& 105\\ \hline\end{array}$
What is the chi-square test-statistic for this data?
${\displaystyle {\chi }^2=}$
Report all answers accurate to three decimal places.