Improve Your Understanding of College Level Statistics Problems

A Bank wishes to determine the mean income of its credit card holders and more specifically wants to investigate whether there are any differences in the mean income between males and females. Confidence interval as a statistical inference method has been considered to respond this objective.
You are required to
1) Comment on the choice of confidence intervals as a statistical inference method for the above. Describe how you will proceed to determine the corresponding confidence intervals.
2) Explain how you would use confidence intervals as evidence suggesting that in average males and females income differ.
Use Numerical examples to illustrate as and when required.
(Word count around 250 words)

Which of the following statements is false?
1) We use one-sample procedures when our samples are equal in size but arent independent
2) Everything else being equal, a confidence interval based on 15 degrees of freedom will be narrower than one based on 10 degrees of freedom.
3) We can pool our estimates of the population variance ifwe want a narrower confidence interval for a given confidence level.
A. None of the above gives the correct response
B. 2 only
C. 1 only
D. 3 only
E. 1 and 2 only

Here are summary statistics fro randomly selected weights of newborn girs:
${\displaystyle n=240,\bar{x}=26.1hg,s=6.3hg}$
Construct a confidence interval estimate of the mean. Use a ${\displaystyle 99\mathrm{\%}}$ confidence level. Are these results very different from the confidence interval
${\displaystyle 25.1hg<\mu <28.1hg}$
with only 13 sample values,
${\displaystyle \bar{x}=26.6hg}$ and ${\displaystyle s=1.8hg?}$
What is the confidence interval for the population mean ${\displaystyle \mu ?}$
Are the results between the two confidence intervals very different?
a) No, because each confidence interval contains the mean of the other confidence interval.
b) No, because the confidence interval limits are similar.
c) Yes, because the confidence interval limits are not similar.
d) Yes, because one confidence interval does not contain the mean of the other confidence interval.

A random sample of 324 medical doctors showed that 164 had a solo practice.
a) Let p represent the proportion of all medical doctors who have a solo practice. Find a point estimate for p. (Use 3 decimal places.)
b) Find a 90% confidence interval for p. (Use 3 decimal places.)
lower limit
upper limit
c) Give a brief explanation of the meaning of the interval.
10% of the confidence intervals created using this method would include the true proportion of physicians with solo practices.
90% of all confidence intervals would include the true proportion of physicians with solo practices.
10% of all confidence intervals would include the true proportion of physicians with solo practices.
90% of the confidence intervals created using this method would include the true proportion of physicians with solo practices.

If you obtained one thousand ${\displaystyle 95\mathrm{\%}}$ confidence intervals for a population mean, ${\displaystyle \mu }$, roughly how many of the intervals would actually contain ${\displaystyle \mu }$?

Matilda has constructed three confidence intervals, all from the same random sample. The confidence levels are ${\displaystyle 95\mathrm{\%},98\mathrm{\%},99.9\mathrm{\%}}$. The confidence intervals are
${\displaystyle 6.4<u<12.3,5.1<u<13.6}$ and ${\displaystyle 6.8<u<11.8}$ Unfortunately, Matilda has forgotten which confidence interval goes with level. Match each confidence interval with its level.
What confidence goes with each the confidence level and indicate whether these confidence intervals are for a population mean or for a population proportion, also include support with the results.

Suppose you conduct a test and your p-value turns out to be 0.08. What can you conclude?
Reject ${\displaystyle H_o}$ at ${\displaystyle \alpha =0.05}$ but not at ${\displaystyle \alpha =0.10}$
a) Reject ${\displaystyle H_o}$ at ${\displaystyle \alpha =0.05}$ but not at ${\displaystyle \alpha =0.10}$
b) Reject ${\displaystyle H_o}$ at ${\displaystyle \alpha =0.01}$ but not at ${\displaystyle \alpha =0.05}$
c) Reject ${\displaystyle H_o}$ at ${\displaystyle \alpha =0.10}$ but not at ${\displaystyle \alpha =0.05}$
d) Reject ${\displaystyle H_o}$ at alpha equal to ${\displaystyle 0.10,0.05,}$ and ${\displaystyle 0.01}$
e) Do not reject ${\displaystyle H_o}$ at ${\displaystyle \alpha }$ equal to ${\displaystyle 0.10,0.05,}$ or ${\displaystyle 0.01}$

Problem 1: A machine is producing metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 cm. Find a 99% confidence interval of the true mean diameter of pieces from this machine, assuming an approximate normal distribution.

Tell, please, what's the difference between the the "population of interest" and "parameter of interest"?

Let ${\displaystyle P_i}$ denote the i-th prime number. Is there any formula for expressing
${\displaystyle S=\sum _{i=1}^m{P}_i}$.
We know that there are around ${\displaystyle \frac{P_m}{\ln \left(P_m\right)}}$ prime numbers less than or equal to ${\displaystyle P_m}$. So, we have:
${\displaystyle S\le m\times P_m\le \frac{P_m^2}{\ln \left(P_m\right)}}$
I want to know, if there is a better bound for S, in the litrature.

The number of viewers of American Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution. What is the probability that next week’s show will:
Have between 30 and 34 million viewers?

You roll a die. If it comes up a 6, you win 100. If not, you gettoroll again. If you get a 6 the second time, you win 50. If not, you lose. Find the expected amount you'll win.

A researcher was interested in knowing whether the mean weight of the second baby is higher, lower, or about the same as the mean weight of the first baby for women who have at least two children

In the article "Graphical Display of Two-Way Contingency Tables", R. Snee presented data on hair color and eye color among 592 students in an elementary statistics course at the University of Delaware. Raw data for that information are presented on the WeissStats site. Use the technology of your choice to do the following tasks, and interpret your results. a) Obtain both a frequency distribution and a relative-frequency distribution for the hair-color data. b) Get a pie chart of the hair-color data. c) Determine a bar chart of the hair-color data. d) Repeat parts (a)-(c) for the eye-color data.

Your math test scores are 68, 78, 90, and 91.
What is the lowest score you can earn on the next test and still achieve an average of at least 85?
Getting an Answer Solve your inequality to find the lowest score you can earn on the next test and still achieve an average of at least 85.
What score do you need to earn?

Ron Larson - Calculus 11th Edition
Chp 3.3 Increasing and decreasing functions and the first derivative test.
Please show work and explain steps, thank you.
Modeling Data. The end-of-year assets of the Medicare Hospital Insurance Trust Fund (in billions of dollars) for the years 2006 through 2014 are shown.
2006: 305.4 2007: 326.0 2008: 321.3
2009: 304.2 2010: 271.9 2011: 244.2
2012: 220.4 2013: 205.4 2014: 197.3
(Source: U.S. Centers for Medicare and Medicaid Services)
(b) Use a graphing utility to plot the data and graph the model.

Look at the normal curve below, and find ${\displaystyle \mu ,\mu +\sigma }$, and ${\displaystyle \sigma }$
$$\begin{array}{|ccc|}\hline \mu & =& \\ \mu +\sigma & =& \\ \sigma & =& \\ \hline\end{array}$$

The data for the joint probability mass function of X and Y (two different measurement systems) are given in the table below.
a) Calculate the marginal distributions of X and Y and plot them.
b) Select one of the Y values from the table and find the conditional probability mass function of X for that Y value you have selected and plot it.
c) Show whether X and Y are independent or not.
$$\begin{array}{|ccccc|}\hline f(x,y)& 1& 2& 3& 4\\ 15& 0.1& 0& 0.1& 0.05\\ 20& 0.05& 0.05& 0& 0.1\\ 25& 0& 0.05& 0.05& 0.1\\ 30& 0.1& 0.05& 0.15& 0.05\\ \hline\end{array}$$
d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).