Improve Your Understanding of College Level Statistics Problems

Calculate the confidence intervals for the ratio of the two population variances and the ratio of standard deviations. Suppose the samples are simple random samples taken from normal populations.
a. ${\displaystyle \alpha =0.05,n_1=30,s_1=16.37,n_2=39,s_2=9.88,}$
b. ${\displaystyle \alpha =0.01,n_1=25,s_1=5.2,n_2=20,s_2=6.8}$

Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United States in 1979 and by the Stockholm Convention on Persistent Organic Pollutants in 2001: One study, published in 1972 by R. Risebrough, is titled “Effects of Environmental Pollutants Upon Animals Other Than Man”. In that study, 50 Anacapa pelican eggs were collected and measured for their shell thickness, in millimetres (mm), and concentration of PCBs, in parts per million (ppm). a) Obtain a scatterplot for the data. b) Decide whether finding a regressimz 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.

The service life in kilometer of Goody tires is assumed to follow a normal distribution with a standard deviation of 5,000 km. A random sample of 25 tires yielded a mean service life of 30,000 km. 1) Find the ${\displaystyle 95\mathrm{\%}}$ confidence interval for the true mean service life. 2) 2. Find a ${\displaystyle 75\mathrm{\%}}$ confidence interval for the true mean service life. 3) Calculate the widths of the intervals found in 1 and 2. How do these widths change as the confidence level decreases?

A two-sample inference deals with dependent and independent inferences. In a two-sample hypothesis testing problem, underlying parameters of two different populations are compared. In a longitudinal (or follow-up) study, the same group of people is followed over time. Two samples are said to be paired when each data point in the first sample is matched and related to a unique data point in the second sample.
This problem demonstrates inference from two dependent (follow-up) samples using the data from the hypothetical study of new cases of tuberculosis (TB) before and after the vaccination was done in several geographical areas in a country in sub-Saharan Africa. Conclusion about the null hypothesis is to note the difference between samples.
The problem that demonstrates inference from two dependent samples uses hypothetical data from the TB vaccinations and the number of new cases before and after vaccination. $\begin{array}{|ccc|}\hline Geographicalregions& Beforevaccination& Aftervaccination\\ 1& 85& 11\\ 2& 77& 5\\ 3& 110& 14\\ 4& 65& 12\\ 5& 81& 10\\ 6& 70& 7\\ 7& 74& 8\\ 8& 84& 11\\ 9& 90& 9\\ 10& 95& 8\\ \hline\end{array}$
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following: Construct a one-sided ${\displaystyle 95\mathrm{\%}}$ confidence interval for the true difference in population means. Test the null hypothesis that the population means are identical at the 0.05 level of significance.

The difference between the qualitative and quantitative data with examples

Determine whether the tests of proportion are used for the categorical or the numerical data.

In a certain small town, 65% of the households subscribe to the daily paper, 37% subscribe to the weekly local paper, and 25% subscribe to both papers. a. Make a two-way table to represent this data. b. If a household is selected at random, what is the probability that it subscribes to at least one of the two papers? Shade these areas in your table. c. Charlie's neighbor subscribes to at least one paper. What is the probability that he receives the daily paper?

Researchers carried out a survey of fourth-, fifth- and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.
$\begin{array}{ccccc}& 4thgrade& 5thgrade& 6thgrade& Total\\ Grades& 49& 50& 69& 168\\ Athletic& 24& 36& 38& 98\\ Popular& 19& 22& 28& 69\\ Total& 92& 108& 135& 335\end{array}$
Suppose we select one of these students at random. What's the probability of each of the following? The student is not a sixth-grader and did not rate good grades as important.

The admissions office of a college wants to determine whether there is a relationship between IQ scores x and grade-point averages y after the first year of school. An equation that models the data obtained by the admissions office is
${\displaystyle y=0.069x-4.755.}$
Estimate the values of x that predict a grade-point average of at least 3.5. (Simplify your answer completely. Round your answer to the nearest whole number.)

What is the difference between a normal profile of a random variable and normal pdf of a random variable. What is the median value of a random variable having a normal pdf.

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm ${\displaystyle {\log }_{2}5}$

The lifespan of a 100-W fluorescent lamp is define to be normally distributed with ${\displaystyle \sigma =30}$ hrs. A random sample of 15 lamps has a mean life of ${\displaystyle x=1000}$ hours.
Construct a $90\mathrm{\%}$ lower-confidence bound on the mean life.

The mean +1 sd of In [calcium intake (mg)] among 25 females, 12 to 14 years of age, below the poverty level is $6.56+0.64.$
Similarly, the mean + 1 sd of In [calcium intake (mg)] among 40 females, 12 to 14 years of age, above the poverty level is $6.80+0.76.$
1) Test for a significant difference between the variances of the two groups.
2) What is the appropriate procedure to test for a signifi- cant difference in means between the two groups?
3) Implement the procedure in Problem 8.3 using the critical-value method.

Gender is on variable of interest in a study of the effectiveness of a new medication.For data entry purposes, the researcher conducting the study assigns 1 for Male and 2 for Female. Is the gender data quantitative or qualtitative?

To Explain:the report about all of these growth rates.

When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 90% confident that the population proportion is estimated to within 0.05? (Round your answer up to the nearest whole number.)

A population of values has a normal distribution with ${\displaystyle \mu =204.3}$ and ${\displaystyle \sigma =43}$. You intend to draw a random sample of size ${\displaystyle n=111}$.
Find the probability that a single randomly selected value is less than 191.2.
${\displaystyle P\left(X<191.2\right)=}$?
Find the probability that a sample of size ${\displaystyle n=111}$ is randomly selected with a mean less than 191.2.
${\displaystyle P\left(M<191.2\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

Indicate whether the following variables are categorical or numerical? If they are numerical, state whether they are discrete or continuous.
(a) The price of randomly selected sweaters in a department store.
(b) The first three digits of the social security number of randomly selected US residents. The eye color of randomly selected Columbia students.
(c) The number of views of randomly selected YouTube videos. The speed of randomly selected cars on Broadway.

Whether the statement is true or false.

What is cross tabulation?