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Recent questions in Confidence intervals

Braxton Pugh 2021-02-26

Consider the function $f (x) = \sin x$ on th interval [0, 3]. Let P be a uniform partition of [0, 3] with 4 sub-intervals. Compute the left and right Riemann sum of f on the partition. Enter approximate values, rounded to three decimal places.

Jaden Easton 2021-02-25

Is America’s romance with movies on the wane? In a Gallup Poll of n = 800 randomly chosen adults, 45% indicated that movies were getting better whereas 43% indicated that movies were getting worse. Find a 98% confidence interval for p, the overall proportion of adults who say that movies are getting better.

Kyran Hudson 2021-02-25

A psychologist is interested in constructing a $99 %$ confidence interval for the proportion of people who accept the theory that a persons

amanf 2021-02-25

Given sample informatio: $\overset{―}{x} = 34, σ = 4, n = 10$ to calculate the following confidence intervals for $μ$ assuming the sample is from a normal population.
99 percent confidence. (Round your answers to 4 decimal places.)

defazajx 2021-02-24

If it was discovered that the average monthly salary earned by a sample of 19 employees of the company was R18 500, with a standard deviation of R1 750, then create a 95% confidence interval for the true average monthly salary earned by all employees of People Plus Pty. Define your response.

nitraiddQ 2021-02-23

Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let j: denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence intervals (7-8, 9.6)
(a) Would 2 90%% confidence interval calculated from this same sample have been narrower or wider than the glven interval? Explain your reasoning.
(b) Consider the following statement: There is 9 95% chance that Is between 7.8 and 9.6. Is this statement correct? Why or why not?
(c) Consider the following statement: We can be highly confident that 95% of al bottles ofthis type of cough syrup have an alcohol content that is between 7.8 and 9.6. Is this statement correct? Why or why not?

usagirl007A 2021-02-23

1. A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 144 students who averaged 44.7 texts per day. The standard deviation was 16.5 texts. a. To compute the confidence interval use a ? z t distribution. b. With 98% confidence the population mean number of texts per day is between and texts. c. If many groups of 144 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day. 2. You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately $σ = 40.4$ dollars. You would like to be 90% confident that your estimate is within 1.5 dollar(s) of average spending on the birthday parties. How many parents do you have to sample? n = 3. You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately $σ = 57.5$ . You would like to be 95% confident that your estimate is within 0.1 of the true population mean. How large of a sample size is required?

Globokim8 2021-02-16

A poll in 2017 reported that 699 out of 1027 adults in a certain country believe that marijuana should be legalized. When this poll about the subject was first conducted in 1969, only 12% of rhe country supported legalizztion. Assume the conditions for using the CLT are met.
a) Find and interpet a 99% confidence interval for the proportion of adults in the country 2017 that believe marijuana should be legalized is (0.643, 0.718)
b) Find and interpret a 90%confidence interval for this population parameter. The 90% confidence interval for the proportion of adults in the country 2017 that believe marijuana should be legalized is (0.657, 0.705)
c)Find the margin of error for each of the confidence intervals found The margin of error of the 99% confidence interval is 0.039 and the margin of error of the 90% confidence interval is 0.025
d) Without computing it, how would the margin of error of an 80% confidence interval compare with the margin of error for 90% and 99% intervals? Construct the 80% confidence interval to see if your production was correct
How would a 80% interval compare with the others in the margin of error?

Clifland 2021-02-13

Use the function $y = 2 x f r o m x = 0 t o x = 1$ and n equal subintervals with the function evaluated at the left-hand endpoint of each subinterval.
a)What is the area of the first rectangle?
b) What is the area of the second rectangle?
c)What is the area of the ith rectangle?

permaneceerc 2021-02-12

What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let $x =$ depth of dive in meters, and let $y =$ optimal time in hours. A random sample of divers gave the following data.
$\begin{array}{cc} x & 13.1 & 23.3 & 31.2 & 38.3 & 51.3 & 20.5 & 22.7 \\ y & 2.78 & 2.18 & 1.48 & 1.03 & 0.75 & 2.38 & 2.20 \end{array}$
(a)
Find $Σ x, Σ y, Σ x^{2}, Σ y^{2}, Σ x y, and r$ . (Round r to three decimal places.)
$Σ x =$
$Σ y =$
$Σ x^{2} =$
$Σ y^{2} =$
$Σ x y =$
$r =$
(b)
Use a $1 %$ level of significance to test the claim that $ρ < 0$ . (Round your answers to two decimal places.)
$t =$
critical $t =$
Conclusion
Reject the null hypothesis. There is sufficient evidence that $ρ < 0$ .Reject the null hypothesis. There is insufficient evidence that $ρ < 0$ .
Fail to reject the null hypothesis. There is sufficient evidence that $ρ < 0$ .Fail to reject the null hypothesis. There is insufficient evidence that $ρ < 0 .$
(c)
Find $S_{e}, a, and b$ . (Round your answers to four decimal places.)
$S_{e} =$
$a =$
$b =$

Reeves 2021-02-11

I have a question:
With the given sample, you want to calculate the population mean $μ$ .
54.7
48.9
56.3
43.5
41.5
41.2
54.2
You think the population is dispersed normally. Find the 99.99 percent confidence level range. Put your response in parenthesis as an open-interval that is accurate to two decimal places (because the sample data are reported accurate to one decimal place).
$99.9 % C . I . = (35.68, 61.54)$ Incorrect
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Rivka Thorpe 2021-02-10

Suppose you have selected a random sample of ? $= 14$ measurements from a normal distribution. Compare the standard normal ? values with the corresponding ? values if you were forming the following confidence intervals.
a) $95 %$ confidence interval
$? =$
$? =$
b) $80 %$ confidence interval
$? =$
$? =$
c) $98 %$ confidence interval
$? =$
$? =$

remolatg 2021-02-09

The lifespan of a 100-W fluorescent lamp is define to be normally distributed with $σ = 30$ hrs. A random sample of 15 lamps has a mean life of $x = 1000$ hours.
Construct a $90 %$ lower-confidence bound on the mean life.

Rui Baldwin 2021-02-09

The service life in kilometer of Goody tires is assumed to follow a normal distribution with a standard deviation of 5,000 km. A random sample of 25 tires yielded a mean service life of 30,000 km. 1) Find the $95 %$ confidence interval for the true mean service life. 2) 2. Find a $75 %$ confidence interval for the true mean service life. 3) Calculate the widths of the intervals found in 1 and 2. How do these widths change as the confidence level decreases?

Ernstfalld 2021-02-09

Calculate the confidence intervals for the ratio of the two population variances and the ratio of standard deviations. Suppose the samples are simple random samples taken from normal populations.
a. $α = 0.05, n_{1} = 30, s_{1} = 16.37, n_{2} = 39, s_{2} = 9.88,$
b. $α = 0.01, n_{1} = 25, s_{1} = 5.2, n_{2} = 20, s_{2} = 6.8$

Yasmin 2021-02-06

You may need to use the appropriate appendix table or technology to answer this question.
Money reports that the average annual cost of the first year of owning and caring for a large dog in 2017 is $1,448. The Irish Red and White Setter Association of America has requested a study to estimate the annual first-year cost for owners of this breed. A sample of 50 will be used. Based on past studies, the population standard deviation is assumed known with $σ = $ 230 .$
$\begin{matrix} 1, 902 & 2, 042 & 1, 936 & 1, 817 & 1, 504 & 1, 572 & 1, 532 & 1, 907 & 1, 882 & 2, 153 \\ 1, 945 & 1, 335 & 2, 006 & 1, 516 & 1, 839 & 1, 739 & 1, 456 & 1, 958 & 1, 934 & 2, 094 \\ 1, 739 & 1, 434 & 1, 667 & 1, 679 & 1, 736 & 1, 670 & 1, 770 & 2, 052 & 1, 379 & 1, 939 \\ 1, 854 & 1, 913 & 2, 163 & 1, 737 & 1, 888 & 1, 737 & 2, 230 & 2, 131 & 1, 813 & 2, 118 \\ 1, 978 & 2, 166 & 1, 482 & 1, 700 & 1, 679 & 2, 060 & 1, 683 & 1, 850 & 2, 232 & 2, 294 \end{matrix}$
(a)
What is the margin of error for a $95 %$ confidence interval of the mean cost in dollars of the first year of owning and caring for this breed? (Round your answer to nearest cent.)
(b)
The DATAfile Setters contains data collected from fifty owners of Irish Setters on the cost of the first year of owning and caring for their dogs. Use this data set to compute the sample mean. Using this sample, what is the $95 %$ confidence interval for the mean cost in dollars of the first year of owning and caring for an Irish Red and White Setter? (Round your answers to nearest cent.)
$_ to $__

Jaya Legge 2021-02-01

Suppose $f (x) = 2 x^{3} .$ Write an expression in terms of x and h that represents the average rate of change of f over any interval of length h. [That is, over any interval (x, x + h)] Simplify your answer as much as possible.

Khadija Wells 2021-01-31

Consider the function $f (x) = x^{2}$ on the interval [1, 9]. Let P be a uniform partition of [1,9] with 16 sub-intervals. Compute the left and right Riemann sum of f on the partition. Use exact values.

rocedwrp 2021-01-31

True or False? A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants were recruited into the study and randomized to receive an experimental drug or a placebo. The primary outcome is a reduction in self-reported symptoms. Among 50 participants who receive the experimental medication, 30 report a reduction of symptoms as compared to 15 participants of 50 assigned to the placebo. The $95 %$ CI for the relative risk of participants reporting a reduction of symptoms between the experimental and placebo groups is between 1.529 and 8.012.

Falak Kinney 2021-01-31

Sketch a graph of $y = 2 x o n [- 1, 2]$ and use geometry to find the exact value of function given
$\int_{- 1}^{2} 2 x d x$

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