Statistical Inference

Problem 1301

13. Each person in a simple random sample of 2,000 received a survey, and 317 people returned their survey. How could nonresponse cause the results of the survey to be biased? (A) Those who did not respond reduced the sample size, and small samples have more bias than large samples. (B) Those who did not respond caused a violation of the assumption of independence. (C) Those who did not respond were indistinguishable from those who did not receive the survey. (D) Those who did not respond represent a stratum, changing the simple random sample into a stratified random sample. (E) Those who did respond may differ in some important way from those who did not respond.

See Solution

Problem 1302

A researcher conducted an experiment to investigate the effectiveness of a medicated lotion in treating a skin irritation. A group of 80 people with a history of skin irritation volunteered for the study. Of the 80 people, 40 were randomly assigned the medicated lotion, and the remaining 40 were given a nonmedicated lotion. At the end of one month, the skin irritation had cleared for 36 people ( 90 percent) using the medicated lotion and 16 people ( 40 percent) using the nonmedicated lotion. Analysis of the results showed the difference was statistically significant. What can be concluded from the experiment? A) Treating the skin irritation with the medicated lotion will cause the irritation to clear. (B) There was no difference in the effectiveness of the two lotions because 28 people still had the skin irritation. (C) Any conclusion is problematic because the participants were volunteers and were not randomly selected from the population.
D There is enough evidence to conclude that the medicated lotion is more effective than the nonmedicated lotion in treating the skin irritation.

See Solution

Problem 1303

Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a $t$ -statistic will be used for inference about the difference in sample means. State the degrees of freedom used.
Find the endpoints of the $t$ -distribution with $5 \%$ beyond them in each tail if the samples have sizes $n_{1}=8$ and $n_{2}=10$ . Enter the exact number for the degrees of freedom and round your answer for the endpoints to two decimal places. degrees of freedom = $\square$ endpoints $= \pm \mathbf{i}$

See Solution

Problem 1304

1 The administration of AT\&T Stadium would like to determine which snack food is most preferred at football games held in the stadium. For a select game, a computer program is used to generate a list of 200 seat numbers. The purchasers of the tickets for those seats are contacted and asked about their favorite snack food. Is the sample a good representation of the population?
A Yes, because the sample contains 200 people B Yes, because the sample is random and representative of the people who attend football games at AT\&T Stadium C No, because the sample is not randomly selected D No, because the sample is not representative of all people who attend football games at AT\&T Stadium
2 The coaches of a school football team want to know how many families from the school plan to attend this week's game. Each coach takes a different approach to obtain this information. Which sampling method would provide a good representation of the population? Select TWO correct answers. A Choose every fourth student from an alphabetical list of the entire student body and ask if their families will attend the game. B Stop every fifth car that enters the school parking lot one morning to ask if their families will attend the game. C Ask all the students in the last period PE class if their families will attend the game. D Call all the parents of the football players to ask if their families will attend the game. E Use a numbered list of all students in the school and a random number generator on a calculator to choose students to ask if their families will attend the game.
3 Last week Carlos surveyed customers leaving Mega Food. Of the 500 people surveyed, 447 said that Mega Food was their favorite grocery store. From these survey results, Carlos concluded that Mega Food was the favorite grocery store among all the people in his town. Which is the best explanation for why his conclusion might not be valid?
A The sample may not have been representative of all the people in Carlos' town. B Carlos asked every customer coming out of the store rather than asking every fifth customer who left the store. C The survey Carlos used did not ask how old the customers were. D The sample size was too small due to the population of the town being small.
4 The city council plans to conduct a survey and use the results to improve city services. The council wants to select citizens at random to participate in the survey. Which sampling method will NOT produce results representative of the population?
A Obtain a list of customer names from the water department and survey each member of every tenth household over the age of 18 B Survey every person who attends a city council meeting each month for six months C Survey each member of households with even house numbers. D Use a computer program to generate a list of addresses.

See Solution

Problem 1305

\begin{align} \text{A data set is given below.} \\ (a) & \text{ Draw a scatter diagram. Comment on the type of relation that appears to exist between } x \text{ and } y. \\ (b) & \text{ Given that } \bar{x}=3.8333, s_{x}=2.1370, \bar{y}=3.7167, s_{y}=1.7371, \text{ and } r=-0.9473, \\ & \text{ determine the least-squares regression line.} \\ (c) & \text{ Graph the least-squares regression line on the scatter diagram drawn in part (a).} \\ \begin{array}{ccccccc} \hline \mathbf{x} & 1 & 2 & 3 & 5 & 6 & 6 \\ \hline \mathbf{y} & 5.1 & 5.6 & 5.1 & 2.7 & 1.7 & 2.1 \\ \hline \end{array} \end{align} (a) \text{ Choose the correct graph below.} \\ \text{A.} \\ \text{B.} \\ \text{C.} \\ \text{D.} \\ \text{The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.} \\ \text{Dialogue Transcript:} \\ \text{assistant:} \\ \text{It looks like you're asking about a math problem involving a scatter diagram and a least-squares regression line. However, I see that part (a) mentions choosing the correct graph, but it doesn't show the options A, B, C, or D. Could you please describe what each graph option looks like, or let me know which part of the problem you would like help with? This way, I can assist you more effectively!} \\ \text{user:} \\ \text{skip (a)}

See Solution

Problem 1306

29. A 2002 study states that Canadians spent an average of 3.2 hours online. A sociologist thinks that this value has increased and collects information on a random sample of 150 Canadians. This group spends an average of 3.6 hours online, with standard deviation 1.3 hours. What description best fits this situation? (A) This is a one population mean test with $\mu=3.2$ and $\bar{x}=3.6$ . (B) This is a one population mean test with $\mu=3.6$ and $\bar{x}=3.2$ . (C) This is a two population mean test with $\mu_{1}=3.2$ and $\mu_{2}=3.6$ . (D) This is a two population mean test with $\bar{x}_{1}=3.2$ and $\bar{x}_{2}=3.6$ . (E) This is a two population mean test with $\mu_{1}=3.2$ and $\bar{x}_{2}=3.6$ .
Answer: $\qquad$

See Solution

Problem 1307

How does changing the confidence level affect the width of a confidence interval?
How does sample size relate to the width of a confidence interval?

See Solution

Problem 1308

3. Identify a potential problem with each sampling method. a) Suppose you want to know whether most people enjoy shopping. You survey the shoppers at a local mall. b) The cook in the school cafeteria surveys the teachers to find out which items to sell. c) To determine public opinion on the effectiveness of the local police force, residents in the area with the greatest crime rate are surveyed. d) To find out about the exercise habits of Canadian teenagers, a fitness magazine asks its readers to email information about their exercise habits.
4. a) In each case, will the selected sample represent the population? Explain. i) To find out if the arena should offer more public skating times, a survey is posted on a bulletin board in the arena and left for patrons to complete. ii) To find out the favourite breakfast food of grade 9 students, a survey of 300 randomly-selected grade 9 students was conducted. iii) To find out if the soccer league should buy new uniforms for the players, 20 parents of the students in the soccer league were surveyed. b) If the sample does not represent the population, suggest another sample that would. Describe how you would select that sample.
5. Assessment Focus Suppose you want to find out how people feel about lowering the age at which teens can drive. a) Describe a sampling method that would not lead to valid conclusions. Justify your choice. b) Describe a sampling method you might use, and justify your choice.
6. a) Explain how you might obtain each sample. i) a simple random sample from the school population ii) a systematic sample of cell phones from a factory iii) a cluster sample of teenagers from your town iv) a stratified random sample of apple trees in an orchard b) Suggest a topic of data collection for each sample in part a.

See Solution

Problem 1309

A random sample of 835 births included 426 boys. Use a 0.05 significance level to test the claim that $50.5 \%$ of newborn babies are boys. Do the results support the belief that $50.5 \%$ of newborn babies are boys?
Identify the null and altemative hypotheses for this test. Choose the correct answer below. A. $H_{0}: p=0.505$ $H_{1}: p \neq 0.505$ B. $H_{0}: p=0.505$ $H_{1}: p<0.505$ c. $\begin{array}{l} H_{0}: p=0.505 \\ H_{1}: p>0.505 \end{array}$ D. $H_{0}: p \neq 0.505$ $H_{1}: p=0.505$

See Solution

Problem 1310

4. It has been estimated that the G-car obtains a mean of 35 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 36 G -cars and records the mileage obtained for each car over a driving course similar to that used to obtain the estimate. The following data resulted: $\bar{x}=36.8$ miles per gallon, $s=6$ miles per gallon. Calculate the value of $\beta$ if the true value of the mean is 37 miles per gallon. Use $\alpha=0.025$ .

See Solution

Problem 1311

QUESTION 10 A random sample of 15 long distance runners aged $20-25$ was selected from a running club. The resting heart rates (in beats per minute) of the runners are shown below. Assuming $\sigma=8.03$ , give the $95 \%$ and $98 \%$ confidence intervals for the population mean. \begin{tabular}{|l|l|l|l|l|} \hline 62 & 70 & 61 & 64 & 75 \\ \hline 75 & 70 & 62 & 66 & 79 \\ \hline 67 & 62 & 66 & 69 & 70 \\ \hline \end{tabular}
Round answers to one decimal place $\mathrm{Cl}_{95 \%}$ : Lower Limit $=$ $\square$ ：Upper Limit = $\square$ Cl98\%: Lower Limit $=$ $\square$ ; Upper Limit = $\square$

See Solution

Problem 1312

```latex فرض کنید می‌خواهیم تعداد اصابت گلوله‌های سه نوع سلاح انفرادی را با هم مقایسه کنیم. اصابت گلوله‌های هر کدام از این سلاح‌ها در پنج روز به شرح زیر بوده است:
\begin{align} \text{A:} & \quad 26, 19, 21, 10, 24 \\ \text{B:} & \quad 19, 22, 28, 16, 30 \\ \text{C:} & \quad 22, 18, 13, 21, 21 \\ \end{align}
در سطح معنی‌دار ۵ درصد آزمون کنید که آیا اختلاف معنی‌داری بین میانگین‌های تعداد اصابت گلوله‌های سه نوع اسلحه وجود دارد یا خیر؟ برای این منظور چهار مرحله آزمون تحلیل واریانس را تکمیل نمایید.
۱. تعریف فرض‌ها: - فرض صفر ( $H_0$ ): میانگین تعداد اصابت گلوله‌ها برای هر سه نوع سلاح برابر است. - فرض یک ( $H_1$ ): حداقل یکی از میانگین‌ها با دیگران متفاوت است.
۲. آماره آزمون: - جدول تحلیل واریانس: \begin{tabular}{|c|c|c|c|c|} \hline \text{منبع تغییرات} & \text{مجموع توان‌های دوم} & \text{درجه آزادی} & \text{میانگین توان‌های دوم} & \text{آماره آزمون} \\ \hline \text{تیمارها} & \text{SS(tr)} = 18 & & \text{MS(tr)} = \ldots & F = \ldots \\ \text{خطا} & \text{SSE} = \ldots & & \text{MSE} = \ldots & \\ \hline \text{جمع} & \text{SST} = 586 & & & \\ \hline \end{tabular}
۳. مقدار بحرانی:
۴. تصمیم‌گیری: - با توجه به مقدار آماره آزمون و مقدار بحرانی، تصمیم بگیرید که آیا فرض صفر رد می‌شود یا خیر.

See Solution

Problem 1313

* Problem 2
Groundwater well is known to begin pumping sand once it becomes exploited (old), and this may damage the subsequent water treatment processes. To solve this problem, two alternatives are proposed: - A new well can be drilled at a capital cost of $\$ 580,000$ with minimal operating and maintenance expenses of $\$ 11,500$ per year. - A settling tank can be constructed ahead of the treatment processes which will cost $\$ 230,000$ to build and $\$ 42,400$ per year to operate and maintain.
The salvage value of either option at EOY 20 is $10 \%$ of the capital investment. Using a MARR of $5 \%$ .

See Solution

Problem 1314

Find the residual for a 29 g chick from an egg with a breadth of 40 mm using the equation $\hat{y}=-47+2x$ .

See Solution

Problem 1315

The average American gets a haircut every 37 days. Is the average smaller for college students? The data below shows the results of a survey of 13 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. $42,30,26,24,26,40,42,29,23,27,24,29,32$
What can be concluded at the the $\alpha=0.01$ level of significance level of significance? a. For this study, we should use t-test for a population mean 0 b. The null and alternative hypotheses would be: $H_{0}$ : $\mu 0$ E $\square$ $\square$ $0^{6}$ $0^{6}$
0 $0^{6}$ c. The test statistic $\square$ $\left.t^{2}\right)^{2}=$ (please show your answer to 3 decimal places.) $\square$ d. The p -value $=$ $\square$ (Please show your answer

See Solution

Problem 1316

На рынке подсластителей торгуются сироп топинамбура и стевия. Какое значение может принимать перекрёстная эластичность спроса на сироп топинамбура по цене стевии, е? Выберите ВСЕ верные ответы. (Частично правильный вариант не засчитывается!) a. $\mathrm{e}<0$ b. $e>1$ c. $\mathrm{e}=0$ d. $0<e<1$

See Solution

Problem 1317

Что вероятнее всего произойдет в экономике в долгосрочном периоде после перманентного повышения доли государственных расходов на потребление в ВВП?
Выберите один ответ: a. рост профицита госбюджета b. снижение уровня безработицы c. увеличение объема выпуска d. повышение темпа инфляции

See Solution

Problem 1318

Show how you arrived at your solution on the answer sheet for full credit. Write neatly and be organized. 8
PROBCEM 6 Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used lo classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of $\mu=16.4$ feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 36 waves showed an average wave height of $\bar{x}=17.3$ feets. Previous studies of severe storms indicate that $\sigma=3.5$ feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating?
Use the 0.01 level of significance and the $\mathbf{P}$ - Value method a.) Hypotheses (5 points): $\begin{array}{l} H_{0} \cdot \mu=16.4 \text { feet } \\ H_{a} \cdot \mu>16.4 \text { feet } \end{array}$
Levelot S Sandicance: $\alpha=0.01$ Sample sie $n=36$ $z=\frac{0.9}{3.5 / 6}=\frac{0.9}{0.5833} \approx 1.51 \sqrt{n}$ $P(z>1.54) \approx 0.0618$ d.) Decision ( 5 points):
Since the $P$ -value 0.0618 is greater than the sio level $a=0.01$ , we fail to reject the null hypo e.) Conclusion (5 points)

See Solution

Problem 1319

Question $\mathbf{J}$ Not yet answered Marked out of 1.00
The $90^{t h}$ percentile of the standard normal distribution is a. 2.05 b. 1.645 C. 1.96 d. 1.28

See Solution

Problem 1320

Question: Poisson Distribution
Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent and identically distributed (i.i.d.) random variables, where each $X_{i}$ follows a Poisson distribution with parameter $\lambda>0$ . The probability mass function (PMF) for a Poisson random variable is given by:
Likelihood Estimation fo $f_{X}(x ; \lambda)=\frac{\lambda^{x} e^{-\lambda}}{x!}, \quad x=0,1,2, \ldots$ where $\lambda$ is the rate parameter of the Poisson distribution. (a) Write the likelihood function $L(\lambda)$ for the sample $X_{1}, X_{2}, \ldots, X_{n}$ . (b) Derive the log-likelihood function $\ell(\lambda)=\ln L(\lambda)$ . (c) Find the Maximum Likelihood Estimator (MLE) for $\lambda$ by solving $\frac{\partial e(\lambda)}{\partial \lambda}=$ 0 . (d) Verify that the second derivative of the log-likelihood function at the MLE is negative, confirming that the MLE is indeed a maximum. (e) Find the Fisher information for $\lambda, I(\lambda)=-E\left[\frac{\partial^{2} \ell(\lambda)}{\partial \lambda^{2}}\right]$ . (f) Using the MLE and Fisher information, calculate the Cramer-Rao lower bound for the variance of the MLE.

See Solution

Problem 1321

Question: Sufficient Estimator for Poisson Distribution
Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample from a ${ }^{* *}$ Poisson distribution** with an unknown parameter $\lambda$ , where $\lambda>0$ . The probability mass function (PMF) of each $X_{i}$ is given by: $f(x ; \lambda)=\frac{\lambda^{x} e^{-\lambda}}{x!}, \quad x=0,1,2, \ldots$ (a) Write the likelihood function $L(\lambda)$ based on the random sample $X_{1}, X_{2}, \ldots, X_{n}$ . (b) Use the ${ }^{* *}$ Factorization Theorem** to show that the statistic $T=\sum_{i=1}^{n} X_{i}$ is a ${ }^{* }$ sufficient statistic ${ }^{ }$ for $\lambda$ . (c) Find the ${ }^{ }$ maximum likelihood estimator (MLE) ${ }^{ }$ of $\lambda$ . (d) Show that the statistic $T=\sum_{i=1}^{n} X_{i}$ is a ${ }^{ *}$ complete and sufficient** statistic for $\lambda$ . Justify your answer.

See Solution

1 ...11 12 13 14

Statistical Inference

Problem 1301

Problem 1302

Problem 1303

Problem 1304

Problem 1305

Problem 1306

Problem 1307

How does changing the confidence level affect the width of a confidence interval?
How does sample size relate to the width of a confidence interval?

Problem 1308

Problem 1309

Problem 1310

Problem 1311

Problem 1312

Problem 1313

Problem 1314

Find the residual for a 29 g chick from an egg with a breadth of 40 mm using the equation $\hat{y}=-47+2x$ .

Problem 1315

Problem 1316

Problem 1317

Problem 1318

Problem 1319

Question $\mathbf{J}$ Not yet answered Marked out of 1.00
The $90^{t h}$ percentile of the standard normal distribution is a. 2.05 b. 1.645 C. 1.96 d. 1.28

Problem 1320

Problem 1321

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Statistical Inference

Problem 1301

Problem 1302

Problem 1303

Problem 1304

Problem 1305

Problem 1306

Problem 1307

How does changing the confidence level affect the width of a confidence interval?How does sample size relate to the width of a confidence interval?

Problem 1308

Problem 1309

Problem 1310

Problem 1311

Problem 1312

Problem 1313

Problem 1314

Find the residual for a 29 g chick from an egg with a breadth of 40 mm using the equation y^=−47+2x\hat{y}=-47+2xy^​=−47+2x.

Problem 1315

Problem 1316

Problem 1317

Problem 1318

Problem 1319

Question J\mathbf{J}J Not yet answered Marked out of 1.00The 90th90^{t h}90th percentile of the standard normal distribution is a. 2.05 b. 1.645 C. 1.96 d. 1.28

Problem 1320

Problem 1321

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

How does changing the confidence level affect the width of a confidence interval?
How does sample size relate to the width of a confidence interval?

Find the residual for a 29 g chick from an egg with a breadth of 40 mm using the equation $\hat{y}=-47+2x$ .

Question $\mathbf{J}$ Not yet answered Marked out of 1.00
The $90^{t h}$ percentile of the standard normal distribution is a. 2.05 b. 1.645 C. 1.96 d. 1.28