Improve Your Understanding of College Level Statistics Problems

The ANOVA technique is designed to evaluate the null hypothesis that: a) Two populations have equal variance b) The mean of each treatment group is no different from the mean of the pooled population c) The mean square error (MSE) of the treatment group is larger than the overall MSE Write down the sum of squares decomposition and explain, briefly, in your own words how the sum of squares decomposition is used to conduct statistical inference in ANOVA.

A random sample of U.S. adults was recently asked, "Would you support or oppose major new spending by the federal government that would help undergraduates pay tuition at public colleges without needing loans?" The two-way table shows the responses, grouped by age.

$\begin{array}{ccc}& AgeResponse& \begin{array}{lrrrrr}& 18-34& 35-49& 50-64& 65+& Total\\ Support& 91& 161& 272& 332& 856\\ Oppose& 25& 74& 211& 255& 565\\ Do{n}^{\prime }tknow& 4& 13& 20& 51& 88\\ Total& 120& 248& 503& 638& 1509\end{array}\end{array}$

Do these data provide convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults?

The perimeter of a triangular plot of land is 2400ft. The longest side is 200 ft less than twice the shortest. The middle side is is 200 ft ,ess than the longest side. Finde the lengths of the three sides of the triangular plot

Explain how to find the range of a data set. 1)What is an advantage of using the range as a measure of variation? 2)What is a disadvantage?

For the same data, null hypothesis, and level of significance, is it possible that a one-tailed test results in the conclusion to reject Hg while a two tilled test results in the conclusion to fail to reject Ho? Explain.

Is the gift you purchased for that special someone really appreciated? This was the question investigated in the Journal of Experimental Social Psychology (Vol. 45, 2009). Toe researchers examined the link between engagement ring price (dollars) and level of appreciation of the recipient ${\displaystyle (\text{measured on a 7-point scale where}1=\text{"not at all" and}7=\text{to a great extent"}).}$ Participants for the study were those who used a popular Web site for engaged couples. The Web site's directory was searched for those with "average" American names (e.g., "John Smith," "Sara Jones"). These individuals were then invited to participate in an online survey in exchange for a $10 gift certificate. Of the respondents, those who paid really high or really low prices for the ring were excluded, leaving a sample size of 33 respondents.a) Identify the experimental units for this study.b) What are the variables of interest? Are they quantitative or qualitative in nature?c) Describe the population of interest.d) Do you believe the sample of 33 respondents is representative of the population? Explain. e. In a second, designed study, the researchers investigated whether the link between gift price and level of appreciation was stronger for birthday gift givers than for birthday gift receivers. Toe participants were randomly assigned to play the role of gift-giver or gift-receiver. Assume that the sample consists of 50 individuals. Use a random number generator to randomly assign 25 individuals to play the gift-receiver role and 25 to play the gift-giver role.

Use the technology of your choice to do the following tasks. The National Oceanic and Atmospheric Administration publishes temperature and precipitation information for cities around the world in Climates of the World. Data on average high temperature (in degrees Fahrenheit) in July and average precipitation (in inches) in July for 48 cities are on the WeissStats CD. For part (d), predict the average July precipitation of a city with an average July temperature of ${\displaystyle {83}^{\circ }F}$ a) Construct and interpret a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation. d) Make the indicated predictions. e) Compute and interpret the correlation coefficient. f) Identify potential outliers and influential observations.

Consider a set of 20 independent and identically distributed uniform random variables in the interval (0,1). What is the expected value and variance of the sum, S, of these random variables?
Select one:
a.${\displaystyle E\left(S\right)=10}$, ${\displaystyle Var\left(S\right)=1.66667}$
b.${\displaystyle E\left(S\right)=200}$, ${\displaystyle Var\left(S\right)=16.6667}$
c.${\displaystyle E\left(S\right)=100}$, ${\displaystyle Var\left(S\right)=200}$
a.${\displaystyle E\left(S\right)=10}$, ${\displaystyle Var\left(S\right)=12}$

Whether the statement is true or false. Rewrite it as a true statement if it is false.

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

The tables show the battery lives (in hours) of two brands of laptops. a) Make a double box-and-whisker plot that represents

A researcher has gathered information from a random sample of 178 households. For each of the following variables, construct confidence intervals to estimate the population mean. Use the 90% level. a. An average of 2.3 people resides in each household. Standard deviation is 0.35. b. There was an average of 2.1 television sets (s
0.10) and 0.78 telephones (s
0.55) per household. c. The households averaged 6.0 hours of television viewing per day (s
3.0)

CNBC recently reported that the mean annual cost of auto insurance is $998. Assume the standard deviation is $298.
Find the probability that a single randomly selected value is less than $985.
${\displaystyle P\left(X<985\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

The presidential election is coming. Five survey companies (A, B, C, D, and E) are doing survey to forecast whether or not the Republican candidate will win the election. Each company randomly selects a sample size between 1000 and 1500 people. All of these five companies interview people over the phone during Tuesday and Wednesday. The interviewee will be asked if he or she is 18 years old or above and U.S. citizen who are registered to vote. If yes, the interviewee will be further asked: will you vote for the Republican candidate? On Thursday morning, these five companies announce their survey sample and results at the same time on the newspapers. The results show that a% (from A), b% (from B), c% (from C), d% (from D), and e% (from E) will support the Republican candidate. The margin of error is plus/minus 3% for all results. Suppose that ${\displaystyle c>a>d>e>b}$. When you see these results from the newspapers, can you exactly identify which result(s) is (are) not reliable and not accurate? That is, can you identify which estimation interval(s) does (do) not include the true population proportion? If you can, explain why you can, if no, explain why you cannot and what information you need to identify. Discuss and explain your reasons. You must provide your statistical analysis and reasons.

For this study, why we would want to use Chi-Squared?
1.A study investigating the effects of second-hand smoke in working environments asked the following question: “How often do you experience second-hand smoke in a work environment/function? Never, Occasionally, Fairly Often, Very Often, Almost Always.” The question was asked of managers and employees to determine whether there was an association between position and the amount of second-hand smoke exposure.

Describe in words the region of $R^3$ represented by the equation(s) or inequality.
$x^2+y^2=4$

Regarding z-scores: a. How is a z-score obtained? b. What is the interpretation of a z-score? c. An observation has a z-score of 2.9. Roughly speaking, what is the relative standing of the observation?

Identify the type of data that would be used to describe a response.
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Quantitative - Continuous
Qualitative (Categorical)
Quantitative - Discrete

Meaning for F and M assumed as independent random variables in context.
F and M are independent random variables.
For F:
Mean,
${\mu }_F=120$