Practice Math Statistics Problems and Master the Concepts

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?

Efan Halliday 2021-09-23

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

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.

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.

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.)

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.

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: $95 %$

Carol Gates 2021-09-19

Find Maximum Volume of a rectangular box that is inscribed in a sphere of radius r.
The part i do not get the solutions manual got $2 x, 2 y$ , and $2 z$ as the volume. Can you explain how the volume of the cube for this problem is $v = 8 x y z ?$

Jason Farmer 2021-09-19

Determine intervals in which solutions are sure to exist. y(4)+4y'''+3y=t

opatovaL 2021-09-18

A standard normal table, also called the unit normal table or Z table, may be a mathematical table for the values of $ϕ$ , which are the values of the cumulative distribution function of the traditional distribution.
$\begin{array}{cc} confidence intervals & Z \\ 90 & 1.645 \\ 95 & 1.96 \\ 96 & 2.05 \\ 97 & 2.17 \\ 98 & 2.326 \\ 99 & 2.576 \end{array}$
a) How do calculate Z-score using the confidence interval?

vestirme4 2021-09-18

In a survey of 2695 adults, 1446 say they have started paying bills electronically in the last year.
Construct a $99 %$ confidence interval for the population proportion.
Interpret your results. Choose the correct answer below.
A) With $95 %$ confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval
B) With $99 %$ confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
C) The endpoints of the given confidence interval show that adults pay bills online $99 %$ of the time.

nitraiddQ 2021-09-18

In a survey of 3307 adults, 1464 say they startied paying bills online in the last year.
Construct a $99 %$ confidence interval for the population proportion.
Interpret your results. Choose the correct answer below.
A) With $95 %$ confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval
B) The endpoints of the given confidence interval show that adults pay bills online $99 %$ of the time.
C) With $99 %$ confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

cistG 2021-09-18

The Level of Significance of a Statistical Test The $R$ and $D$ department of a paint company has developed an additive that it hopes will increase the ability of the company’s stain for outdoor decks to resist water absorption. The current formulation of the stain has a mean absorption rate of 35 units. Before changing the stain, a study was designed to evaluate whether the mean absorption rate of the stain with the additive was decreased from the current rate of 35 units. The stain with the additive was applied to 50 pieces of decking material. The resulting data were summarized to $\overset{―}{x} = 33.6$ and $s = 9.2$
a) Is there substantial evidence $(α = 0.01)$ that the additive reduces the mean absorption from its current value?
b) What is the level of significance (p -value) of your test results?
c) What is the probability of a Type II error if the stain with the additive in fact has a mean absorption rate of 30?
d) Estimate the mean absorption using a 99% confidence interval. Is the confidence interval consistent with your conclusions from the test of hypotheses?

Isa Trevino 2021-09-17

A set of data consists of 45 observations between 0 and 29. Which size would you advise for the class period?

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