Improve Your Understanding of College Level Statistics Problems

Makes inferences about populations using data drawn from the population. Instead of using the entire population to gather the data, the statistician will collect a sample or samples from the millions of residents and make inferences about the entire population using the sample. histogram population mean descriptive statistics inferential statistics

Determine whether the situation involves comparing proportions for two groups or comparing two proportions from a single group. Then state whether the parameter of interest is in population proportions. For a population of all LCCC students, we would like to compare the proportion of students who use a Windows-based PC to the proportion who use a Mac. This situation involves ? and the parameter of interest is ? For a population of all registered voters in the United States, we would like to compare the males who voted in the last election to the proportion of females who voted in the last election. This situation involves ? and the parameter of interest is ?

Use either the critical-value approach or the P-value approach to perform the required hypothesis test. Approximately 450,000 vasectomies are performed each year in the United States. In this surgical procedure for contraception, the tube carrying sperm from the testicles is cut and tied. Several studies have been conducted to analyze the relationship between vasectomies and prostate cancer. The results of one such study by E. Giovannucci et al. appeared in the paper “A Retrospective Cohort Study of Vasectomy and Prostate Cancer in U.S. Men” (Journal of the American Medical Association, Vol. 269(7), pp. 878-882). Of 21,300 men who had not had a vasectomy, 69 were found to have prostate cancer, of 22,000 men who had had a vasectomy, 113 were found to have prostate cancer. a. At the 1% significance level, do the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer? b. Is this study a designed experiment or an observational study? Explain your answer. c. In view of your answers to parts (a) and (b), could you reasonably conclude that having a vasectomy causes an increased risk of prostate cancer? Explain your answer.

From the Statistical Abstract of the United States, we obtained data on percentage of gross domestic product (GDP) spent on health care and life expectancy, in years, for selected countries. 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.

Give a full answer to given question

1) An independent-measures study uses ?

2) An independent-measures study uses two samples, each with $n=13$, to compare two treatment conditions. What is the df value for the t statistic for this study?

For each of the following situations, state whether you’d use a chi-square goodness-of-fit test, a chi-square test of homogeneity, a chi-square test of independence, or some other statistical test:
a) Is the quality of a car affected by what day it was built? A car manufacturer examines a random sample of the warranty claims filed over the past two years to test whether defects are randomly distributed across days of the work week.
b) A medical researcher wants to know if blood cholesterol level is related to heart disease. She examines a database of 10,000 patients, testing whether the cholesterol level (in milligrams) is related to whether or not a person has heart disease.
c) A student wants to find out whether political leaning (liberal, moderate, or conservative) is related to choice of major. He surveys 500 randomly chosen students and performs a test.

A new vaccine was tested to see if it could prevent the ear infections that many infants suffer from. Babies about a year old were randomly divided into two groups. One group received vaccinations, and the other did not. The following year, only 328 of 2460 vaccinated children had ear infections, compared to 508 of 2453 unvaccinated children. Complete parts a) through c) below. a) Are the conditions for inference satisfied? A. Yes. The data were generated by a randomized experiment, less than 10% of the population was sampled, the groups were independent, and there were more than 10 successes and failures in each group. B. No. It was not a random sample. C. No. The groups were not independent. D. No. More than 10% of the population was sampled.

The marks of DMT students results in June 2020 sessional examinations were normally disyributed with a mean pass mark of 9 and a standard deviation pass mark of 0.15. After moderation, a sample of 30 papers was selected to see if the mean pass mark had changed. The mean pass mark of the sample was 8.95. a) Find the ${\displaystyle 95\mathrm{\%}}$ confidence interval of students mean mark. b) Calculate for the critical regions of the ${\displaystyle 95\mathrm{\%}}$ confidence intervals. c) Using your results in "a" and "b" above, is there evidence of a change in the mean pass mark of the DMT students.

To determine: The number of luxury home sales S(t) in a major Canadian urban area over a period of 12 year is given by: ${\displaystyle \Rightarrow S\left(t\right)=5.8t^2-81.2t+1200}$

A random sample of ${\displaystyle n=400}$ students is selected from a population of ${\displaystyle N=4000}$ students to estimate the average weight of the students. The sample mean and sample variance are found to be ${\displaystyle x=140lb\text{and}{s}^2=225.\text{Find the}95\mathrm{\%}(z=2)}$ confident interval.

Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.
$\begin{array}{|cc|}\hline NumberN& Pricep\\ 200& 53.00\\ 250& 52.50\\ 300& 52.00\\ 350& 51.50\\ \hline\end{array}$
(a) Find a formula for p in terms of N modeling the data in the table.
${\displaystyle p=}$
(b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.
${\displaystyle R=}$
Is R a linear function of N?
(c) On the basis of the tables in this exercise and using cost, ${\displaystyle C=35N+900}$, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month.
${\displaystyle P=}$
(d) Is P a linear function of N?

Consider the solid that is bounded below by the cone $z=\sqrt{3x^2+3y^2}$
and above by the sphere $x^2+y^2+z^2=16.$.Set up only the appropriate triple integrals in cylindrical and spherical coordinates needed to find the volume of the solid.

In a one-way ANOVA, what does it mean to reject the statement in the null hypothesis if three treatment groups are being compared?

If a report states that certain data were used to reject a given hypothesis, would it be a good idea to know what type of test (one-tailed or two-tailed) was used? Explain.

To state:The null and alternative hypothesis.

Which of the following statements about the sampling distribution of the sample mean is incorrect?
(a) The standard deviation of the sampling distribution will decrease as the sample size increases.
(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.
(c) The sample mean is an unbiased estimator of the population mean.
(d) The sampling distribution shows how the sample mean will vary in repeated samples.
(e) The sampling distribution shows how the sample was distributed around the sample mean.

A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-50s.

$\begin{array}{ccccc}& \text{ Elite }& \text{ Non-elite }& \text{Did not play }& \text{ Total }\\ \text{ Yes }& 10& 9& 24& 43\\ \text{ No }& 61& 206& 548& 815\\ \text{ Total }& 71& 215& 572& 858\end{array}$
Suppose we choose one of these players at random. What is the probability that the player has arthritis, given that he or she was classified as an elite soccer player?

Let X and Y be Bernoulli random variables. Let $Z=XY$.
a) Show that Z is a Bernoulli random variable.
b) Show that if X and Y are independent, then $P_Z=P_X{P}_Y$.

Determine whether the study depicts an observational study or an experimental study.
A study was done to see if sugar consumption can cause hypoeractivity in children. The researcher took four groups of children and assigned different amounts of sugar the children had to consume. After a certain period of​ time, they assessed whether or not the children were hyperactive.

Find the proportion of professional male golfers-drive on an average of 280 yards or less.
Approximately 5 percent of professional male golfers are found to be less than an average of 280 yards.