Improve Your Understanding of College Level Statistics Problems

A researcher completes a chi-square test for independence and obtains ${\displaystyle {\chi }^2=6.2}$ for a sample of n=40 participants.
a. If the frequency data formed a ${\displaystyle 2\times 2}$ matrix, what is the phi-coefficient for the test?
b. If the frequency data formed a ${\displaystyle 3\times 3}$ matrix, what is the Cramer’s phi-coefficient for the test?
c. Explain why a very small value for an expected frequency can distort the results of chi-square test.

A recent study sought to determine if exercising after studying for an exam may help retain information. The 150 student volunteers that participated in the study were randomly assigned to three groups. All students were given a picture memory task that they studied for 15 minutes. After studying, one of the groups was instructed to exercise for 30 minutes immediately after studying. A second group was instructed to wait 1 hour after studying and then exercise for 30 minutes. The third group was instructed to not exercise after studying. The next day all 150 student volunteers were given a test to determine how well they could remember what they studied. Here are the results:
The researchers want to test: ${\displaystyle H_0}$: There is no difference in the distribution of performance on the test for the three treatment groups among the population of all student volunteers like these.
${\displaystyle H_{\alpha }}$: There is a difference in the distribution of performance on the test for the three treatment groups among the population of all student volunteers like these.
Which test is appropriate in this situation?
(A) chi-square test for homogeneity
(B) chi-square test for association
(C) chi-square test for goodness of fit
(D) two-sample test for p_1-p_2p1​-p2​
(E) matched pairs tt test

$\begin{array}{cc}& \text{Treatment Group}\\ \text{Performance on the Test}& \begin{array}{|ccccc|}\hline & \text{ Exercise immediately }& \text{ Exercise 1 hour later }& \text{ Do not exercise }& \text{ Total }\\ \text{ Less than 50\% }& 6& 8& 25& 39\\ \text{ 50\% to 75\% }& 22& 28& 22& 72\\ \text{ Greater than 75\% }& 22& 14& 3& 39\\ \text{ Total }& 50& 50& 50& 150\\ \hline\end{array}\end{array}$

A random sample of 500 people were classified by their ages into 3 age-groups: 29 years and younger, 30 to 64 years, and 65 years and older. Each person from the sample was surveyed about which of 4 major brands of cell phone they used. Their responses were compiled and displayed in a 3-by-4 contingency table. A researcher will use the data to investigate whether there is an association between cell phone brand and age- group. Which of the following is the appropriate test for the investigation?
a. A one-sample t-test for a population mean
b. A two-sample t-test for a difference between means
c. A chi-square goodness-of-fit test
d. A chi-square test of homogeneity
e. A chi-square test of independence

A preliminary sample of 1200 engineers has been taken, out of which 260 are females. The sample is used to estimate the proportion of female engineers denoted by pF .
Estimate the 95% confidence interval for pF.

A political pollster selects a random sample of 75 registered voters from Allegheny County, Pennsylvania. The city of Pittsburgh is in Allegheny County. The pollster is interested in determining if the distribution of political party preference among registered voters in this county differs between those who live in Pittsburgh and those who live in the suburbs. The responses are displayed in the table.
$\begin{array}{cc}& \text{Political Party}\\ \text{Location}& \begin{array}{|cccc|}\hline & \text{ Democratic }& \text{ Independent }& \text{ Republican }\\ \text{ City }& 20& 8& 11\\ \text{ Suburbs }& 8& 10& 18\\ \hline\end{array}\end{array}$
The pollster would like to know if these data provide convincing evidence of a relationship between residential status and political party in the population of all registered voters in Allegheny County. What is the appropriate inference procedure?
1. chi-square test for goodness of fit because the data come from one random sample
2. chi-square test for homogeneity because the data come from independent random samples
3. chi-square test for association/independence because the data come from one random sample
4. chi-square test for association/independence because the data come from independent random samples

A flight attendant selects a random sample of 201 travelers. For each, he records the class in which the person travels and whether they have carry-on luggage. He would like to know if there is convincing evidence that the class in which a person travels is associated with having carry-on luggage. Let ${\displaystyle \alpha =0.05}$.
What are the hypotheses for this test?
a.${\displaystyle H_0}$: Class is not independent of carry-on luggage. ${\displaystyle H_{\alpha }}$: Class is independent of carry-on luggage.
b. ${\displaystyle H_0}$: Class is independent of carry-on luggage. ${\displaystyle H_{\alpha }}$: Class is not independent of carry-on luggage.
c. ${\displaystyle H_0}$: There is an association between class and carry-on luggage. ${\displaystyle H_{\alpha }}$: There is no association between class and carry-on luggage.
d. ${\displaystyle H_0}$: The proportion of travelers who have carry-on luggage is not the same in the types of class. ${\displaystyle H_{\alpha }}$: The proportion of travelers who have carry-on luggage is the same in the types of class.

A course has 2 sections, Section A and Section B. On the last exam, Section A's 10 students had an average score of 80, and Section B's 20 students had an average score of 90. What is the course average score on that exam?

A clothing manufacturer wants to determine whether customers prefer any specific color over other colors in shirts. He selects a random sample of 100 shirts sold and notes the color. The table below shows the result. At ${\displaystyle \propto =0.05}$, is there a color preference?
$\begin{array}{|cc|}\hline \text{ Color }& \text{ Number Sold }\\ \text{ White }& 43\\ \text{ Blue }& 22\\ \text{ Black }& 16\\ \text{ Red }& 9\\ \text{ Yellow }& 10\\ \hline\end{array}$
What test statistics will be used for this problem?
1. Chi-square test of Independence
2. Spearman rho
3. Chi-square test of goodness fit
4. Pearson
5. ANOVA

A casino has been using six-sided dice obtained from Luckytown Dice Company for some of its games of chance. After a string of unusual rolls, the casino is concerned the dice are not fair (i.e. that distribution of rolls is not equally likely). They take a sample of 300 rolls. The observed counts are below. Calculate the value of the Chi-Square test statistic (Part of the calculations have been done for you). Please enter your answer to 2 decimal places.
$\begin{array}{|cccc|}\hline \text{ Value }& \text{ Observed }& \text{ Expected }& \text{ Contribution to Chi-square Test Statistic=(O-E)^2/E }\\ 1& 36& 50& (36-50{)}^2/50=3.92\\ 2& 48& 50& (48-50{)}^2/50=0.08\\ 3& 50& 50& (50-50{)}^2/50=0\\ 4& 43& 50& (43-50{)}^2/50=0.98\\ 5& 34& 50\\ 6& 89& 50\\ \text{ Total }& 300& 300\\ \hline\end{array}$

Find the amount in a savings account after 12 years if $56,780 is invested at 2.8% interest compounded quarterly.

Kirito is thinking of a number, if you add 7, multiply it by 6, subtract 18, and divide 2 theresult is 57. What is Kirito's number.

We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 176 had kids. Based on this, construct a 99% confidence interval for the proportion, p, of adult residents who are parents in this county.

2–6. Resolve F2 Into Components Along The U And V Axes, And Determine The Magnitudes Of These Components. F2 = 150 N V 30° 30° 45° F1 = 200 N

 

Which of the following is true about the sampling distribution of means?
Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.
Shape of the sampling distribution of means is always the same shape as the population distribution, no matter what the sample size is.
Sampling distributions of means get closer to normality as the sample size increases.
Sampling distributions of means are always nearly normal.

I need to figure out how or where to find the standard deviation and mean for this problem Given that z is a standard normal random variable, compute the following probabilities.
a. P(z≤−1.0)
b. P(z≥−1)
c. P(z≥−1.5)
d. P(−2.5≤z)
e. P(−3

the row of numbers shown below to generate 12 random numbers between 01 and 99 09075 11123 14740 39704 88198 93469 52264 39270

What are the mean and standard deviation of a probability density function given by $Pr(X=k)=\frac{9^k{e}^{-9}}{k!}$ for $k\in \{0,1,2...\mathrm{\infty }\}$?

What are the mean and standard deviation of a probability density function given by $Pr(X=k)=\frac{{14}^k{e}^{-14}}{k!}$ for $k\in \{0,1,2...\mathrm{\infty }\}$?

What does a small standard deviation signify? What does a large standard deviation signify?

What are the mean and standard deviation of a probability density function given by $Pr(X=k)=\frac{{12}^k{e}^{-12}}{k!}$ for $k\in \{0,1,2...\mathrm{\infty }\}$?