Mathematics, 25.07.2019 20:00 uticabadgirl

Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. assume that σ is known to be 36.8 cases per year. find a 90%, 95%, and 98% confidence interval for the population mean annual number of reported larceny cases in such communities. compare the lengths of the confidence intervals. as the confidence levels increase, do the confidence intervals increase in length?

Answers: 1

Show answers

Answers

We are given the following data:

Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22

We are to find the confidence intervals for 90%, 95% and 98% confidence level.

Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.

Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.645* \frac{36.8}{ \sqrt{22}}=110.69$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.645* \frac{36.8}{ \sqrt{22}}=136.51$

Thus the 90% confidence interval will be (110.69, 136.51)

Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.96* \frac{36.8}{ \sqrt{22}}=108.22$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.96* \frac{36.8}{ \sqrt{22}}=138.98$

Thus the 95% confidence interval will be (108.22, 138.98)

Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-2.327* \frac{36.8}{ \sqrt{22}}=105.34$
Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+2.327* \frac{36.8}{ \sqrt{22}}=141.86$

Thus the 98% confidence interval will be (105.34, 141.86)

Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)

As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.

Answer from: Quest

270 books in each shelves

Answer from: Quest

answer: 94

step-by-step explanation: 79+91+92+94+94 = 450 divided by 5 (since there are 5 number that are being added) = 90

Can someone plz answer this last ! i will give brainliest to whoever answers it

Another question on Mathematics

Mathematics, 21.06.2019 19:20

Ab and bc form a right angle at point b. if a= (-3,-1) and b= (4,4) what is the equation of bc?

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

How do you write y-10=2 (x-8) in standard form

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

Answers: 3

Answer

Mathematics, 21.06.2019 22:40

Adeli owner keeps track of the to-go orders each day. the results from last saturday are shown in the given two-way frequency table. saturday's to-go deli orders in person by phone online total pick up 38 25 31 94 delivery 35 28 34 97 total 73 53 65 191 what percent of the to-go orders were delivery orders placed by phone? a. 14.66% b. 38.41% c. 28.87% d. 52.83%

Answers: 2

Answer

You know the right answer?

Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. assume...

Questions

Mathematics, 07.04.2020 16:20

In order to use the Pythagorean Theorem, you must know the length or lengths of the triangle and know that the measure of one of the angles is .

Engineering, 07.04.2020 16:20

Why is it important for drilled shaft contractors to place the concrete soon after drilling the shaft? What detrimental effects can occur if the contr...