What is the value of

Daniaal Sanchez
2021-01-24
Answered

Suppose that the n-th Riemann sum (with n sub-intervals of equal length), for some function f(x) on the intrval [0, 2], is ${S}_{n}=\frac{2}{{n}^{2}}\text{}\times \text{}\sum _{k=1}^{n}\text{}k.$

What is the value of${\int}_{0}^{2}\text{}f(x)\text{}dx?$

What is the value of

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saiyansruleA

Answered 2021-01-25
Author has **110** answers

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asked 2021-01-10

The average zinc concentration recovered from a sample of measurements taken in 36 different locations in a river is found to be 2.6 grams per liter. Find the 95% confidence intervals for the mean zinc concentration in the river. Assume that the population standard deviation is 0.3 gram per liter.

asked 2020-12-27

Consider the next 1000 98% Cis for mu that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of $\mu ?$

What isthe probability that between 970 and 990 of these intervals conta the corresponding value of ? (Hint: Let

Round your answer to four decimal places.)

‘the number among the 1000 intervals that contain What king of random variable s 2) (Use the normal approximation to the binomial distribution

What isthe probability that between 970 and 990 of these intervals conta the corresponding value of ? (Hint: Let

Round your answer to four decimal places.)

‘the number among the 1000 intervals that contain What king of random variable s 2) (Use the normal approximation to the binomial distribution

asked 2021-03-09

In a study of the accuracy of fast food drive-through orders, Restaurant A had 298 accurate orders and 51 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B:

asked 2021-08-09

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

Construct the

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.

asked 2022-04-08

Trouble Understanding the Formal Definition of a Confidence Interval

A$1-\alpha$ confidence interval for a paramater $\theta$ is an interval ${C}_{n}=(a,b)$ where $a=a({X}_{1},\cdots ,{X}_{n})$ and $b=b({X}_{1},\dots ,{X}_{n})$ are functions of the data such that

$\mathbb{P}}_{\theta}(\theta \in {C}_{n})>1-\alpha \text{, for all}\text{}\theta \in \mathrm{\Theta$

If$\theta$ is a vector then we use a confidence set (such as a sphere or an ellipse) instead of an interval.

Question:

While I understand conceptually what a confidence interval is (i.e., a 95% CI means that 95% of experiments will trap the paramater in the interval), I don't understand how this formality is capturing this concept.

In particular, I don't understand what is meant by the notion of${\mathbb{P}}_{\theta}(\theta \in {C}_{n})$ . What is the sample space which P is drawing from? What is the set $\theta \in {C}_{n}$ ? It seems here $\theta$ is being treated both as a fixed value (from the notation Pθ) and as a random variable (by the notation $\theta \in {C}_{n}$ ).

A

If

Question:

While I understand conceptually what a confidence interval is (i.e., a 95% CI means that 95% of experiments will trap the paramater in the interval), I don't understand how this formality is capturing this concept.

In particular, I don't understand what is meant by the notion of

asked 2021-06-10

Can filling car tires with nitrogen instead of compressed air increase gas mileage? Describe how you would design a study to try to answer this question. Be as specific as you can about the details of your study.

asked 2021-02-25

Give a full and correct answer
Why is it important that a sample be random and representative when conducting hypothesis testing?
Representative Sample vs. Random Sample: An Overview
Economists and researchers seek to reduce sampling bias to near negligible levels when employing statistical analysis. Three basic characteristics in a sample reduce the chances of sampling bias and allow economists to make more confident inferences about a general population from the results obtained from the sample analysis or study:
* Such samples must be representative of the chosen population studied.
* They must be randomly chosen, meaning that each member of the larger population has an equal chance of being chosen.
* They must be large enough so as not to skew the results. The optimal size of the sample group depends on the precise degree of confidence required for making an inference.
Representative sampling and random sampling are two techniques used to help ensure data is free of bias. These sampling techniques are not mutually exclusive and, in fact, they are often used in tandem to reduce the degree of sampling error in an analysis and allow for greater confidence in making statistical inferences from the sample in regard to the larger group.
Representative Sample
A representative sample is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicates the larger group according to whatever characteristic or quality is under study.
A representative sample parallels key variables and characteristics of the large society under examination. Some examples include sex, age, education level, socioeconomic status (SES), or marital status. A larger sample size reduced sampling error and increases the likelihood that the sample accurately reflects the target population.
Random Sample
A random sample is a group or set chosen from a larger population or group of factors of instances in a random manner that allows for each member of the larger group to have an equal chance of being chosen. A random sample is meant to be an unbiased representation of the larger population. It is considered a fair way to select a sample from a larger population since every member of the population has an equal chance of getting selected.
Special Considerations:
People collecting samples need to ensure that bias is minimized. Representative sampling is one of the key methods of achieving this because such samples replicate as closely as possible elements of the larger population under study. This alone, however, is not enough to make the sampling bias negligible. Combining the random sampling technique with the representative sampling method reduces bias further because no specific member of the representative population has a greater chance of selection into the sample than any other.
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