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Recent questions in Confidence intervals

Ben Shaver 2021-12-12

If you obtained one thousand $95 %$ confidence intervals for a population mean, $μ$ , roughly how many of the intervals would actually contain $μ$ ?

quiquenobi2v6 2021-12-12

Matilda has constructed three confidence intervals, all from the same random sample. The confidence levels are $95 %, 98 %, 99.9 %$ . The confidence intervals are
$6.4 < u < 12.3, 5.1 < u < 13.6$ and $6.8 < u < 11.8$ 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.

Sinead Mcgee 2021-10-02

A statistics practitlioner took a randoml sample of 54 observations form a population whose standard deviation is 29 and computed the sample mean to be 97.
Note: For each confidence interval, enter your answer in the forem (LCL, UCL). You must include the parentheses and the comma between the confidence limits.
A) Estimate the population mean with $95 %$ confidence.
B) Estimate the population mean with $90 %$ confidence.
C) Estimate the population mean with $99 %$ confidence.

Khaleesi Herbert 2021-10-02

The standard deviation for a population is $σ = 14.8$ . This population's sample of 21 observations yielded a mean value of 139.05. It is well known that the population has a normal distribution.
Round your answers to two decimal places.
1) Make a $99 %$ confidence interval for $μ$ . ( Enter your answer; $99 %$ confidence interval, lower bound ,Enter your answer; $99 %$ confidence interval, upper bound )
2) Construct a $97 %$ confidence interval for $μ$ . ( Enter your answer; $97 %$ confidence interval, lower bound ,Enter your answer; $97 %$ confidence interval, upper bound )
3) Determine a $95 %$ confidence interval for $μ$ . ( Enter your answer; $95 %$ confidence interval, lower bound ,Enter your answer; $95 %$ confidence interval, upper bound )

defazajx 2021-10-01

(1) Seek power series solutions of the given differential equation about the given point $x_{0}$ , find the recurrence relation.
(2) Find the first tour terms in each of two solutions $y_{1} and y_{2}$ (unless the series terminates sooner).
(3) By evaluating the Wronskian $W (y_{1} y_{2}) (x_{0})$ , show that $y_{1} and y_{2}$ form a fundamental set of solutions.
(4) It possible, find the general term in each solution $(1 + x^{2}) y 4 x y^{'} + 6 y = 0, x_{0} = 0$

sagnuhh 2021-09-30

In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 358 trials, the touch therapists were correct 172 times. Complete parts (a) through (d).
a) Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? (Type an integer or a decimal. Do not round.)
b) Using Emily's sample results, what is the best point estimate of the therapists' success rate? (Round to three decimal places as needed.)
c) Using Emily's sample results, construct a $90 %$ confidence interval estimate of the proportion of correct responses made by touch therapists.
Round to three decimal places as needed - ? $< p <$ ?

Sinead Mcgee 2021-09-30

A sample selected from a population gave a sample proportion equal to 0.59 .
Round your answers to three decimal places.
a) Make a $95 %$ confidence interval for p assuming $n = 150$
( Enter your answer; confidence interval assuming $n = 150$ , lower bound ,Enter your answer; confidence interval assuming $n = 150$ , upper bound )
b) Construct a $95 %$ confidence interval for p assuming $n = 600$ . ( Enter your answer; confidence interval assuming $n = 600$ , lower bound ,Enter your answer; confidence interval assuming $n = 600$ , upper bound )
c) Make a $95 %$ confidence interval for p assuming $n = 1275$ . ( Enter your answer; confidence interval assuming $n = 1275$ , lower bound ,Enter your answer; confidence interval assuming $n = 1275$ , upper bound )

Lipossig 2021-09-29

The article “Analysis of the Modeling Methodologies for Predicting the Strength of Air-Jet Spun Yarns” (Textile Res. J., 1997: 39–44) reported on a study carried out to relate yarn tenacity $(y, \in \frac{g}{t e x})$ to yarn count $(x_{1}, \in t e x)$ , percentage polyester $(x_{2})$ , first nozzle pessure $(x_{3}, \in \frac{k g}{c m^{2}})$ , and second nozzle pressure $(x_{4}, \in \frac{k g}{c m^{2}})$ The estimate of the constant term in the corresponding multiple regression equation was 6.121. The estimated coefficients for the four predictors were -0.082, 0.113, 0.256, and -0.219, respectively, and the coefficient of multiple determination was 0.946
a) Assuming that the sample size was $n = 25$ , state and test the appropriate hypotheses to decide whether the fitted model specifies a useful linear relationship between the dependent variable and at least one of the four model predictors.
b) Again using $n = 25$ , calculate the value of adjusted $R^{2}$ .
c) Calculate a 99% confidence interval for true mean yarn tenacity when yarn count is 16.5, yarn contains 50% polyester, first nozzle pressure is 3, and second nozzle pressure is 5 if the estimated standard deviation of predicted tenacity under these circumstances is 0.350.

ringearV 2021-09-29

Using 64 randomly selected phone calls, the average call length was calculated to be 4.2 minutes. It is known from previous studies that the variance of the length of phone calls is $1.44 min^{2}$ . Assuming that the length of calls has a normal distribution
a) estimate an interval estimate of the length of a telephone conversation at the 0.95 confidence level
b) confidence 0.99
c) Compare the length of the two intervals and explain how the length of the interval depends on the confidence level.

Khadija Wells 2021-09-28

Find the average value fave of the function ff on the given interval.
$f (x) = \frac{x^{2}}{{(x^{3} + 30)}^{2}}, x \in [- 3, 3]$

postillan4 2021-09-27

Rock band The Rolling Stones have played scores of concerts in the ltwenty years. For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.12 million dollars.
a) Assuming a population standard deviation groos earnings of 0.51 million dollars, obtain a $99 %$ confidence interval for the mean gross earning of all Rolling Stones concerts (in millions).
b) Which of the following is the correct interpretation for your answer in part (a)?
A) We can be $99 %$ confident that the mean gross earnings for this sample of 30 Rolling Stones concert lies in the interval
B) If we repeat the study many times, $99 %$ of the calculated confidence intervals will contain the mean gross earning of all Rolling Stones concerts.
C) There is a $99 %$ chance that the mean gross earning of all Rolling Stones concert lies in the interval
D) None of the above

ddaeeric 2021-09-27

In a random sample of 25 people, the mean commute time to work was 34.1 minutes and the standard deviation was 7.1 minutes. What is the margin of error of $μ$ ?
Interpret the results.
A) With $80 %$ confidence, it can be said that the population mean commute time as between the bounds of the confidence interval.
B) With $80 %$ confidence, it can be said that the commute time is between the bounds of the confidence interval.
C) It can be said that $80 %$ of people have a commute time is between the bounds of the confidense interval
D) If a large sample of people are taken approximately $80 %$ of them will have commute times between the bounds of the confidence interval.

Alyce Wilkinson 2021-09-26

A simple random sample size of 100 is selected from a population with $p = 0.40$
What is the expected value of $\overset{―}{p}$ ?
What is the standard error of $\overset{―}{p}$ ?
Show the sampling distribution of $\overset{―}{p}$ ?
What does the sampling distribution of $\overset{―}{p}$ show?

Rivka Thorpe 2021-09-23

In a random sample of 24 people, the mean commute time to work was 33.7 minutes and the standard deviation was 7.1 minutes. What is the margin of error of $μ$ ?
Interpret the results.
A) With $90 %$ confidence, it can be said that the population mean commute time as between the bounds of the confidence interval.
B) It can be said that $90 %$ of people have a commute time is between the bounds of the confidense interval
C) With $90 %$ confidence, it can be said that the commute time is between the bounds of the confidence interval.
D) If a large sample of people are taken approximately $90 %$ of them will have commute times between the bounds of the confidence interval.

Rivka Thorpe 2021-09-23

In a survey of 2085 adults in a certain country conducted during a period of economic?
Uncertainty, $63 %$ thought that wages paid to workers in industry were too low. The margin of error was 8 percentage points with $90 %$ confidence.
For parts (1) through (4) below, which represent a reasonable interpretation of the survey results. For those that are not reasonable, explain the flaw.
1) We are $90 %$ confident $63 %$ of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.
A) The interpretation is reasonable.
B) The interpretation is flawed. The interpretation provides no interval about the population proportion.
C) The interpretation is flawed. The interpretation sugguests that this interbal sets the standard for all the other intervals, which is not true.
D) The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
2) We are $82 %$ to $98 %$ confident $63 %$ of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low. Is the interpretation reasonable?
A) The interpretation is reasonable.
B) The interpretation is flawed. The interpretation provides no interval about the population proportion.
C) The interpretation is flawed. The interpretation sugguests that this interbal sets the standard for all the other intervals, which is not true.
D) The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
3) We are $90 %$ confident that the interval from 0.55 to 0.71 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low.
A) The interpretation is reasonable.
B) The interpretation is flawed. The interpretation provides no interval about the population proportion.
C) The interpretation is flawed. The interpretation sugguests that this interbal sets the standard for all the other intervals, which is not true.
D) The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
4) In $90 %$ of samples of adults in the country during the period of economic uncertainty, the proportion who believed wages paid to workers in industry were too low is between 0.55 and 0.71.
A) The interpretation is reasonable.
B) The interpretation is flawed. The interpretation provides no interval about the population proportion.
C) The interpretation is flawed. The interpretation sugguests that this interbal sets the standard for all the other intervals, which is not true.
D) The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

Efan Halliday 2021-09-23

Express the confidence interval $53.5 % < p < 69.7 %$ in the form of $\hat{p} \pm M E \hat{p} \pm M E$

tabita57i 2021-09-22

A certain reported that in a survey of 2006 American adults, $24 %$ said they believed in astrology.
a) Calculate a confidence interval at the $99 %$ confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three decimal places.)
(_, _)
b) What sample size would be required for the width of a $99 %$ CI to be at most 0.05 irresoective of the value of $\hat{p}$ ? (Round your answer up to the nearest integer.)

midtlinjeg 2021-09-20

Find the length of the confidence interval given the following data: (s-sample standard deviation)
a) $s = 2.36$
$n = 350$
confidence level: $99 %$ b) $s = 3.35$
$n = 250$
confidence level: $99 %$
c) $s = 3$
$n = 275$
confidence level: $95 %$

Phoebe 2021-09-20

An online used car company sells second-hand cars. For 30 randomly selected transactions, the mean price is 2800 dollars.
a) Assuming a population standard deviation transaction prices of 130 dollars, obtain a $99 %$ confidence interval for the mean price of all transactions.
b) Which of the following is the correct interpretation for your answer in part (a)?
A) If we repeat the study many times, $99 %$ of the calculated confidence intervals will contain the mean price of all transactions.
B) There is a $99 %$ change that the mean price of all transactions lies in the interval
C) We can be $99 %$ confident that the mean price for this sample of 30 transactions lies in the interval
D) None of the above

York 2021-09-20

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 536 randomly selected Americans surveyed, 441 were in favor of the initiative. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between and . b. If many groups of 536 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about percent will not contain the true population proportion.

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