UkusakazaL
2021-08-10
Answered

To monitor complex chemical processes, chemical engineers will consider key process indicators, which may be just yield but most often depend on several quantities. Before trying to improve a process, 9 measurements were made on a key performance indicator. 123, 106, 114, 128, 113, 109, 120, 102, 111. Assume that the key performance indicator has a normal distribution. (a) Find the sample variance s 2 of the sample. (b) Find a $95\mathrm{\%}$ confidence interval for $\sigma 2$ . (c) Find a $98\mathrm{\%}$ confidence interval for $\sigma$ .

You can still ask an expert for help

question2answer

Answered 2021-08-16
Author has **155** answers

Step 1

(a)

to find variance value

1) add them up

2) square your answer

...and divide by the number of items. we have 9 items ,

set this number aside for a moment.

3) take your set of original numbers from step 1, and square them individually this time

4) subtract the amount in step 2 from the amount in step 3

5) subtract 1 from the number of items in your data set,

6) divide the number in step 4 by the number in step 5. this gives you the variance

----------------------------------------------------------------------------------------

to find standard deviation value

take the square root of your answer from step 6. this gives you the standard deviation 8.3367

Step 2

(b)

CONFIDENCE INTERVAL FOR VARIANCE

since

the two critical values

sample size

confidence interval

Step 3

(c)

to calculate confidence interval for standard deviation

where,

asked 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?

(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?

asked 2021-08-04

A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3900 kilometers.

Assume the distribution of measurements to be approximately normal.

a) Construct a$99\mathrm{\%}$ confidence interval for the average number of kilometers an automobile is driven annually in Virginia.

b) What can we assert with$99\mathrm{\%}$ confidence about the possible size of our error if we estimate the average number of kilometers driven by car owners in Virginia to be 23,500 kilometers per year?

Assume the distribution of measurements to be approximately normal.

a) Construct a

b) What can we assert with

asked 2021-08-12

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

Round to three decimal places as needed - ?

asked 2021-08-03

A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is $\sigma =15$

a) Compute the$95\mathrm{\%}$ confidence interval for the population mean. Round your answers to one decimal place.

b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a$95\mathrm{\%}$ confidence interval for the population mean. Round your answers to two decimal places.

c) What is the effect of a larger sample size on the interval estimate?

Larger sample provides a-Select your answer-largersmallerItem 5 margin of error.

a) Compute the

b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a

c) What is the effect of a larger sample size on the interval estimate?

Larger sample provides a-Select your answer-largersmallerItem 5 margin of error.

asked 2022-03-23

Let $X}_{1},\text{}\cdots ,{X}_{n$ be a random sample from a normal distribution with known mean $\mu$ and unknown variance $\sigma}^{2$ . Three possible confidence intervals for $\sigma}^{2$ are

a)$(\sum _{i=1}^{n}\frac{{({X}_{i}-\stackrel{\u2015}{X})}^{2}}{{a}_{1}},\text{}\sum _{i=1}^{n}\frac{{({X}_{i}-\stackrel{\u2015}{X})}^{2}}{{a}_{2}})$

b)$(\sum _{i=1}^{n}\frac{{({X}_{i}-\mu )}^{2}}{{b}_{1}},\text{}\sum _{i=1}^{n}\frac{{({X}_{i}-\mu )}^{2}}{{b}_{2}})$

c)$(\frac{n{(\stackrel{\u2015}{X}-\mu )}^{2}}{{c}_{1}},\text{}\frac{n{(\stackrel{\u2015}{X}-\mu )}^{2}}{{c}_{2}})$

where$a}_{1},\text{}{a}_{2},\text{}{b}_{1},\text{}{b}_{2},\text{}{c}_{1},\text{}{c}_{2$ are constants.

Find values of these six constants which give confidence level 0.90 for each of the three intervals when$n=10$ and compare the expected widths of the tree intervels in this case

With${\sigma}^{2}=1$ , what value of n is required to achieve a $90\mathrm{\%}$ confidence interval of expected width less than 1 in cases (b) and (c) above?

a)

b)

c)

where

Find values of these six constants which give confidence level 0.90 for each of the three intervals when

With

asked 2021-10-02

The standard deviation for a population is $\sigma =14.8$ . A sample of 21 observations selected from this population gave a mean equal to 139.05. The population is known to have a normal distribution.

Round your answers to two decimal places.

a) Make a$99\mathrm{\%}$ confidence interval for $\mu$ . ( Enter your answer; $99\mathrm{\%}$ confidence interval, lower bound ,Enter your answer; $99\mathrm{\%}$ confidence interval, upper bound )

b) Construct a$97\mathrm{\%}$ confidence interval for $\mu$ . ( Enter your answer; $97\mathrm{\%}$ confidence interval, lower bound ,Enter your answer; $97\mathrm{\%}$ confidence interval, upper bound )

c) Determine a$95\mathrm{\%}$ confidence interval for $\mu$ . ( Enter your answer; $95\mathrm{\%}$ confidence interval, lower bound ,Enter your answer; $95\mathrm{\%}$ confidence interval, upper bound )

Round your answers to two decimal places.

a) Make a

b) Construct a

c) Determine a

asked 2022-03-26

Confidence interval when both $\mu$ and $\sigma}^{2$ are unknown

I have the following problem in my problem book:

Let$X\sim N(\mu ,{\sigma}^{2})$ where both $\mu$ and $\sigma}^{2$ are unknown. I have to find a confidence interval for the mean.

What I have so far:

I know that when$\sigma}^{2$ is unknown I can use t-distribution for finding a confidence interval, i.e.:

$\stackrel{\u2015}{x}\pm {t}_{n-1}^{\cdot}\frac{s}{\sqrt{n}},$

where$t}_{n-1}^{\cdot$ is a t-distribution with $n-1$ degrees of freedom and $\stackrel{\u2015}{x}$ is the sample mean from a sample of size n.

The whole problem seems kind of vague to me. Is this enough for describing the confidence interval? I don't know the sample mean$\stackrel{\u2015}{x}$ so is it okay to describe the solution in such a way?

I have the following problem in my problem book:

Let

What I have so far:

I know that when

where

The whole problem seems kind of vague to me. Is this enough for describing the confidence interval? I don't know the sample mean