Improve Your Understanding of College Level Statistics Problems

In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel.
$\begin{array}{lc}& \text{Class}\\ \text{Survived}& \begin{array}{cccc}& \text{ First }& \text{ Second }& \text{ Third }\\ \text{ Yes }& 197& 94& 151\\ \text{ No }& 122& 167& 476\end{array}\end{array}$
Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P (not a passenger in first class and survived).

ACTIVITY H: Sampling Theory and Estimation of Parameters
1. A random sample of 50 students in Holy Angel University shows that they spend an average of 3 hours per day on social media apps with a standard deviation of 0.5 hours. Assume a normal distribution. Construct a ${\displaystyle 90\mathrm{\%}}$ and ${\displaystyle 97\mathrm{\%}}$ confidence interval for the average number of hours spent on social media apps per day.
2. A study was conducted in which two types of fried chicken, Jollibee and KFC, were compared. Number of fried chickens sold, was measured. 90 Jollibee branches were surveyed while 80 were surveyed for KFC. The average fried chicken sold was 7,020 for Jollibee and 8,100 fried chickens for KFC. Find a ${\displaystyle 94\mathrm{\%}}$ and ${\displaystyle 98\mathrm{\%}}$ confidence interval on .Assume that the population standard deviations are 1000 and 500 for KFC and ????--?????????Jollibee, respectively.
3. The following are the average lengths of today’s top 10 Global Spotify hits, in minutes. 3.02, 2.85, 3.33, 3.43, 2.9, 2.93, 3.23, 2.77, 2.45, and 2.88. Find a ${\displaystyle 95\mathrm{\%}}$ confidence interval for the variance of the lengths of this generation’s music, assuming a normal population.

Nurses wondered if birth weights of babies are going up. They knew that the average bith weight ofa baby last year was 7.6 pounds. A random sample of 15 weights of babies atthe hospital where the nurses work gave an average birth weight of 7.9 pounds. Nurses felt thatthe birth Weights this year ware normally distributed. Which ofthe following is true about the distribution of sample means?
Choose the correct answer below.
A. Even though the sample size is less than 30, the distribution of sample means will be normal because the population data follow a normal distribution.
B. The distribution of sample means will be normal regardless of the shape of the data in the population.
C. Since the sample size is less than 30, the population data cannot be normally distributed. Therefore, the distribution of sample means will not be normally distributed.
D. The distribution of sample means will not be normal even though the population data followed a normal distribution because the sample size is less than 30.

Learning math The Core Plus Mathematics Project (CPMP) is an innovative approach to teaching Mathematics that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compare the performances of CPMP students with those taught using a traditional curriculum. In one test, students had to solve applied Algebra problems using calculators. Scores for 320 CPMP students were compared to those of a control group of 273 students in a traditional Math program. Computer software was used to create a confidence interval for the difference in mean scores. (Journal for Research in Mathematics Education, 31, no. 3[2000]) Conf level: 95% Variable: Mu(CPMP) – Mu(Ctrl) Interval: (5.573, 11.427)
a) What’s the margin of error for this confidence interval?
b) If we had created a 98% CI, would the margin of error be larger or smaller?c) Explain what the calculated interval means in context.
d) Does this result suggest that students who learn Mathematics with CPMP will have significantly higher mean scores in Algebra than those in traditional programs? Explain.

Consider the following data set below. Find the UPPER INTERVAL of the population mean at ${\displaystyle 80\mathrm{\%}}$ confidence interval. (write your answer in two decimal places) Given: 12,10,9,11

Confidence Intervals. In Exercises 9–24, construct the confidence interval estimate of the mean.
Genes Samples of DNA are collected, and the four DNA bases of A, G, C, and T are coded as 1, 2, 3, and 4, respectively. The results are listed below. Construct a 95% confidence interval estimate of the mean. What is the practical use of the confidence interval?
2 2 1 4 3 3 3 3 4 1

An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year’s economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments.
$\begin{array}{|ccc|}\hline & Strong& Weak\\ Certificateofdeposit& 6,000& 6,000\\ Officecomplex& 15,000& 5,000\\ Landspeculation& 33,000& -17,000\\ Technicalschool& 5,500& 10,000\\ \hline\end{array}$
Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land speculation, and technical school, respectively. Then V, W, X, and Y are random variables. Assume that next year’s economy has a 40% chance of being strong and a 60% chance of being weak. a. Find the probability distribution of each random variable V, W, X, and Y. b. Determine the expected value of each random variable. c. Which investment has the best expected payoff? the worst? d. Which investment would you select? Explain.

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 101.0 min. After​ treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a ${\displaystyle 95\mathrm{\%}}$ confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
Construct the ${\displaystyle 95\mathrm{\%}}$ confidence interval estimate of the mean wake time for a population with the treatment.
$min<\mu <min$ ​(Round to one decimal place as​ needed.)
What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the​ treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect.

Customers randomly selected at a grocery store included 172 women and 45 men. 74 of the women and 12 of the men used coupons. Find the ${\displaystyle 95\mathrm{\%}}$ confidence interval.

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 200 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.3 seats. ${\displaystyle s_x=?,n=?,n-1=?}$. Construct a ${\displaystyle 92\mathrm{\%}}$ confidence interval for the population average number of unoccupied seats per flight. (State the confidence interval. (Round your answers to two decimal places.)

Your client from question 4 decides they want a ${\displaystyle 90\mathrm{\%}}$ confidence interval instead of a ${\displaystyle 95\mathrm{\%}}$ one. To remind you - you sampled 36 students to find out how many hours they spent online last week. Your sample mean is 46. The population standard deviation, ${\displaystyle \sigma }$, is 7.4. What is the ${\displaystyle 90\mathrm{\%}}$ confidence interval for this sample mean? Keep at least three decimal places on any intermediate calculations, then give your answer rounded to 1 decimal place, with the lower end first then upper.
(_______ , ___________ )

The scores of a certain population on the Wechsler Intelligence Scale for children (WISC) are thought to be normally distributed with a mean and standard deviation of 10. A simple random sample of twenty -five children from this population is taken and each is given the WISC. The mean of the twenty-five score is ${\displaystyle \bar{x}=104.32}$. Based on these data a ${\displaystyle 95\mathrm{\%}}$ confidence interval for ${\displaystyle \mu }$ is computed.
The ${\displaystyle 95\mathrm{\%}}$ confidence interval for ${\displaystyle \mu }$ is?

What is modeling with linear equations?

Explain what is the test statistic used for constructing confidence interval on a proportion.

a. Locate the critical points of ƒ.
b. Use the First Derivative Test to locate the local maximum and minimum values.
c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).
${\displaystyle f\left(x\right)=\frac{x^2}{x^2-1}}$ on ${\displaystyle [-4,4]}$

Based on a simple random sample of 1300 college students, it is found that 299 students own a car. We wish to construct a ${\displaystyle 90\mathrm{\%}}$ confidence interval to estimate the proportions ? of all college students who own a car.
A) Read carefully the text and provide each of the following:
The sample size ${\displaystyle ?=}$
from the sample, the number of college students who own a car is ${\displaystyle ?=}$
the confidence level is ${\displaystyle CL=}$ ${\displaystyle \mathrm{\%}}$.
B) Find the sample proportion ${\displaystyle \widehat{?}=}$
and ${\displaystyle \widehat{?}=1-\widehat{?}=}$

We walk from Central Park to Empire State Building with a constant speed. Our speed X is a random variable uniformly distributed between 3 and 4.5 km/h. The distance is 3 km. Calculate the probability distribution of the total walking time T:
a. Calculate the CDF of T from the distribution of X.
b. Calculate the PDF of T from irs CDF.
Don't forget to specify the intervals for these functions explicitly.

Express the confidence interval ${\displaystyle (0.412,0.789)}$ in the form of ${\displaystyle \hat{p}\pm E}$.

From a simple random sample of 14 shoppers surveyed, the sample mean of money spent for holiday gifts was 145 dollars with a sample standard deviation of 11 dollars. We wish to construct a ${\displaystyle 99\mathrm{\%}}$ confidence interval for the population mean of money spent for holiday gifts.
Read carefully the text and provide each of the following:
The sample size ${\displaystyle ?=}$,
the sample mean ${\displaystyle ?\equiv }$,
the sample standard deviation ${\displaystyle ?=}$, NKS the confidence level ${\displaystyle CL=\mathrm{\%}}$.

Assume that the true value, that is the population mean, the average height of french women in france is 167.5 cm. Students in a class of 160 students each took a random sample of french women of size 100, measured the height of the women and calculated a 95% confidence interval (confidence interval) for the average height.How many students can be expected to calculate a confidence interval that does not include the number 167.5?
15 8 5 20 1