Improve Your Understanding of College Level Statistics Problems

Does a higher state per capita income equate to a higher per capita beer consumption? From the document Survey of Current Business, published by the U.S. Bureau of Economic Analysis, and from the Brewer’s Almanac, published by the Beer Institute, we obtained data on personal income per capita, in thousands of dollars, and per capita beer consumption, in gallons, for the 50 states and Washington, D.C. 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.

The sampling distribution of $\frac{S_1^2}{S_2^2}$ is the ${\chi }^2$ distribution. Give a correct answer true or false inference for two population variances is done through their difference.

Choose an appropriate test from the list of five tests for the given case.

Two different ways to express $\left[\begin{array}{c}1\\ 1\end{array}\right]$
as a linear combination of $v_1,c_{2}and{v}_3.$

Give a full and correct answer for this questions: a.What is the null hypothesis? b.Copy and paste the data into the Group 1 and Group 2 data boxes. Do the distributions look different to you? c.Record the p-value of the hypothesis test. How do you interpret this result?

A car has a purchase price of $24,800. The value declines continuously at an exponential rate of %23 annually. A. Wat is an equation modeling the value of this car after t years? B. What is its value after 6 years? c. How long will it take for its value to be $2000? 2. A bacteria colony grows continuously at an exponential rate. There are initially 1.1 million sent. After 5 days, there are 6.8 million present . a. What is the an equation modeling the number of bacteria present after d days? b. How many bacteria will be present after 7 days? c. How long will it take the number of bacteria to reach 92 million?

A population of values has a normal distribution with ${\displaystyle \mu =49}$ and ${\displaystyle \sigma =79.5}$. You intend to draw a random sample of size ${\displaystyle n=84}$.
Find the probability that a single randomly selected value is greater than 72.4.
${\displaystyle P\left(X>72.4\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

As access to computers becomes more and more prevalent, we see the P-value reported in hypothesis testing more frequently. Review the use of the P-value in hypothesis testing. What is the difference between the level of significance of a test and the P-value? Considering both the P-value and level of significance. under what conditions do we reject or fail to reject the null hypothesis?

Find inequalities that describe the solid and state the coordinate system used. Position the solid on the coordinate system such that the inequalities are as simple as possible. "The solid that remains after a hole 1 inch in diameter is drilled through the center of a sphere 6 inches in diameter "

Decresing the sample size, while holding the confidence level and the variance the same, will do what to the length of wour confidence interval?

Identify the appropriate hypothesis test for each of the following research situations using the options: The null hypothesis, The Test Statistics, The Sample Statistic, The Standard Error, and The Alpha Level.
A researcher conducts a cross-sectional developmental study to determine whether there is a significant difference in vocabulary skills between 8-year-old and 10-year-old children. A researcher determines that 8% of the males enrolled in Introductory Psychology have some form of color blindness, compared to only 2% of the females. Is there a significant relationship between color blindness and gender?
A researcher records the daily sugar consumption and the activity level for each of 20 children enrolled in a summer camp program. The researcher would like to determine whether there is a significant relationship between sugar consumption and activity level.
A researcher would like to determine whether a 4-week therapy program produces significant changes in behavior. A group of 25 participants is measured before therapy, at the end of therapy, and again 3 months after therapy.
A researcher would like to determine whether a new program for teaching mathematics is significantly better than the old program. It is suspected that the new program will be very effective for small-group instruction but probably will not work well with large classes. The research study involves comparing four groups of students: a small class taught by the new method, a large class taught by the new method, a small class taught by the old method, and a large class taught by the old method.

The owner of a large equipment rental company wants to make a rather quick estimate of the average number of days a piece of ditch-digging equipment is rented out per person per time. The company has records of all rentals, but the amount of time required to conduct an audit of all accounts would be prohibitive. The owner decides to take a random sample of rental invoices. Fourteen different rentals of ditch-diggers are selected randomly from the files, yielding the following data. She wants to use these data to construct a $99\mathrm{\%}$ confidence interval to estimate the average number of days that a ditch-digger is rented and assumes that the number of days per rental is normally distributed in the population. Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.
DATA: 3 1 3 2 5 1 2 1 4 2 1 3 1 1

In each of the following, identify the variables are categorical nominal, or categorical ordinal, or numerical discrete or numerical continuous.
2.Pant size of a randomly selected male as S, M, L, XL, XXL.

Round each z-score to the nearest hundredth.
A data set has a mean of
${\displaystyle x=6.8}$
and a standard deviation of 2.5. Find the z-score.
${\displaystyle x=9.0}$

What is frequency distribution?

True or false: The mean, median, and mode can all be used with quantitative data. Explain your answer

To give:the hypotheses for the test.

Describe the five-step p-value approach to hypothesis testing.

Find the correlation between years and cognition.
Find the p-value for testing the correlation.