Improve Your Understanding of College Level Statistics Problems

The entrance of a tunnel can be modeled by ${\displaystyle y=-\frac{11}{50}(x-4)(x-24)}$ where x and y are measured in feet. The x-axis represents the ground. Find the width of the tunnel at ground level.

Given $f(x)\cos (2x)$ and the interval
$[0,3\frac{\pi }{4}]$
approximate the area bounded by the graph of f(x) and the axis on the interval using a left, right, and mid point Riemann sum with $n=3$

Plot the given point $(-4,0)$ in a rectangular coordinate system.

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.

Give a real-life example of data which could have the following probability distributions
Solve a) bimodal distibution
b) uniform distribution
c) exponential distribution
only early

A population of values has a normal distribution with ${\displaystyle \mu =197}$ and ${\displaystyle \sigma =68}$. You intend to draw a random sample of size ${\displaystyle n=181}$
Find the probability that a sample of size ${\displaystyle n=181}$ is randomly selected with a mean between 198.5 and 205.6.
${\displaystyle P\left(198.5<M<205.6\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

Critical Thinking: One-Tailed versus Two-Tailed Tests For the same data and null hypothesis, is the P-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain.

$\overline{)\begin{array}{cc}& HouseworkHours\\ Gender& SampleSize& Mean& StandardDeviation\\ Women& 473473& 33.133.1& 14.214.2\\ Men& 488488& 18.618.6& 15.715.7\end{array}}$

a. Based on this​ study, calculate how many more hours per​ week, on the​ average, women spend on housework than men.

b. Find the standard error for comparing the means. What factor causes the standard error to be small compared to the sample standard deviations for the two​ groups? The cause the standard error to be small compared to the sample standard deviations for the two groups.

c. Calculate the​ 95% confidence interval comparing the population means for women Interpret the result including the relevance of 0 being within the interval or not. The​ 95% confidence interval for ​${\displaystyle ({\mu }_W-{\mu }_M)}$ is: (Round to two decimal places as​ needed.) The values in the​ 95% confidence interval are less than 0, are greater than 0, include 0, which implies that the population mean for women could be the same as is less than is greater than the population mean for men.

d. State the assumptions upon which the interval in part c is based. Upon which assumptions below is the interval​ based? Select all that apply.

A.The standard deviations of the two populations are approximately equal.

B.The population distribution for each group is approximately normal.

C.The samples from the two groups are independent.

D.The samples from the two groups are random.

Situations comparing two proportions are described. In each case, determine whether the situation involves comparing proportions for two groups or comparing two proportions from the same group (1 point each) a. Compare the proportion of U.S. adults who have a positive opinion about the media versus those who have a negative opinion about the media. A) Comparing proportions for two groups B) Comparing two proportions from the same group b. Compare the proportion of female students at a university who live in a dorm to the proportion of male students at a university who live in a dorm A) Comparing proportions for two groups B) Comparing two proportions from the same group

Prove an example of two independent samples and another example of dependent samples providing your reasoning To compare two means or two proportions, one works with two groups. The group are classfied either aas independent or matched pairs. Independent groups meam that the two samples taken are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. The parameter tested using matched pairs is the population mean. The parameters tested using independent groups are either population means or population proportion.

A population of values has a normal distribution with ${\displaystyle \mu =154.5}$ and ${\displaystyle \sigma =96.1}$. You intend to draw a random sample of size ${\displaystyle n=134}$.
Find the probability that a single randomly selected value is greater than 167.
${\displaystyle P\left(X>167\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

To describe:It is possible that the given claim is true or not.
To describe:The questions that should ask about how the data were collected.

Suppose that, for a sample of pairs of observations from two variables, the linear correlation coefficient, r , is negative. Does this result necessarily imply that the variables are negatively linearly correlated?

A chi square test tells us:
a. Whether two continuous variables are correlated with each other.
b. Whether two discrete variables are independent of each other
c. The amount of variation in one variable explained by the other
d. Which categories of one variable are associated with which categories of the other variable

The following table shows the average yearly tuition and required fees, in thousand of dollars, charged by a certain private university in the school year beginning in the given year.
$\begin{array}{|cc|}\hline \text{Year}& \text{Average tuition}\\ 2005& \$17.6\\ 2007& \$18.1\\ 2009& \$19.5\\ 2011& \$20.7\\ 2013& \$21.8\\ \hline\end{array}$
What prediction does the formula modeling this data give for average yearly tuition and required fees for the university for the academic year beginning in 2019?

The vector x is in $H=Span{v}_1,v_2$
and find the beta-coordinate vector $[x{]}_{\beta }$

The table shows the temperatures T (in degrees Fahrenheit) at which water boils at selected pressures p (in pounds per square inch). A model that approximates the datais: ${\displaystyle T=87.97+34.96\text{In}p+7.91\sqrt{p}}$ a) Use a graphing untility to plot the data and graph the model in the same veiwing window. How well does the model fit the data? b) Use the graph to estimate the pressure at which the boiling point of water is  ${300}^{\circ }$ F. c) Calculate T when the pressure is 74 pounds per square inch. Verify your answer graphically.

Give a full answer to given question: Double-stranded DNA looks a little like a ladder that has been twisted into a helix, or spiral. The side supports (poles) of the ladder are ?

To Explain:Linearity of expectation of random variables.

What is the decision at a 0.05 level of significance for each of the following tests?
F(3, 26) = 3.00
Retain or reject the null hypothesis?
F(4, 55) = 2.54
Retain or reject the null hypothesis?
F(4, 30) = 2.72
Retain or reject the null hypothesis?
F(2, 12) = 3.81
Retain or reject the null hypothesis?