Improve Your Understanding of College Level Statistics Problems

For a population with a mean of ${\displaystyle \mu =100}$ and a standard deviation of ${\displaystyle \sigma =20}$,
Find the X values.
${\displaystyle z=-.50}$.

Identify the population: An education professor wants to gather information about parental involvement in early education for students attending a particular Ivy League university. She obtains a list of registered students from the registrar's office and randomly chooses 300 students to study.

Explain and give a full and correct answer how confusing the two (population and a sample) can lead to incorrect statistical inferences.

Give full and correct answer for this questions Pooled variance is appropriately applied in which of the following scenarios? A)When comparing the mean of a treatment on a single group B)When comparing the mean of a treatment on two groups C)When comparing the means of three or more treatments on two groups D)When comparing the means of two treatments on three or more groups

The Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeissStats CD for those presidents who are not still living at the time of this writing. a) Obtain 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 for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed population with mean 62 and standard deviation 4.5?

Let ${\displaystyle X\sim N(6,4)}$.Find the probabilities ${\displaystyle P\left(X<3\right)}$.

True or False? A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants were recruited into the study and randomized to receive an experimental drug or a placebo. The primary outcome is a reduction in self-reported symptoms. Among 50 participants who receive the experimental medication, 30 report a reduction of symptoms as compared to 15 participants of 50 assigned to the placebo. The $95\mathrm{\%}$ CI for the relative risk of participants reporting a reduction of symptoms between the experimental and placebo groups is between 1.529 and 8.012.

Sketch a graph of $y=2xon[-1,2]$ and use geometry to find the exact value of function given
${\int }_{-1}^{2}2xdx$

Consider the function $f(x)=x^2$ on the interval [1, 9]. Let P be a uniform partition of [1,9] with 16 sub-intervals. Compute the left and right Riemann sum of f on the partition. Use exact values.

This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function $p(x)=\frac{1}{{\sqrt{2\pi }}^{\sigma }}{e}^{-(x-\mu {)}^2}/(2{\sigma }^2)$ where $\pi =3.14159265...$ and sigma and mu are constants called the standard deviation and the mean, respectively. Its graph$(\text{for}\sigma =1\text{and}\mu =2)$is shown in the figure. With $\sigma =5\text{and}\mu =0$, approximate ${\int }_0^{+\mathrm{\infty }}p(x)dx.$

The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: "Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, some what agree, some what disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, 120 said that they some what agree, 165 said they some what disagree, and 755 said they strongly disagree with this statement.
Do the responses for this statement provide categorical or quantitative data?

In 1912 the luxury liner Titanic struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. The two-way table gives information about adult passengers who survived and who died, by class of travel. Check the conditions for performing a chisquare test for association.
$\begin{array}{lcccc}& \text{ First }& \text{ Second }& \text{ Third }& \text{ Total }\\ \text{ Survived }& 197& 94& 151& 442\\ \text{ Died }& 122& 167& 476& 765\\ \text{ Total }& 319& 261& 627& 1207\end{array}$

In a study designed to see whether a controlled diet could retard the process of arteriosclerosis, a total of 846 randomly chosen persons were followed over an eight year period. Half were instructed to eat only certain foods, the other half could eat whatever they wanted. At the end of eight years, sixty-six persons in the diet group were found to have died of either myocardial infarction or cerebral infarction, as compared to ninety-three deaths of a similar nature in the control group. Do the appropriate analysis. Let $\alpha =0.05$

Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?

To compare two population means, ${\displaystyle {\mu }_1}$ and ${\displaystyle {\mu }_2}$ we use the information from the samples.

The standard deviation of daily iron intake in the larger population of 9-to 11-year-old boys was 5.56 mg. We want to test whether the standard deviation from the low-income group is comparable to that of the general population

To find: The probability of getting same number of men in two groups.
Given:
A group consists of 6 men and 6 women. Divide into groups 6 in each.

Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be a great danger to natural ecosystems. In a study by R. W. Risebrough titled “Effects of Environmental Pollutants Upon Animals Other Than Man” (Proceedings of the 6th Berkeley Symposium on Mathematics and Statistics, VI, University of California Press, pp. 443-463), 60 Anacapa pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and concentration of PCBs, in parts per million (ppm). a) Obtain 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 for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

Find the range and IQR of the data.