#### Question Details

[answered] MACT 3224/317: Assignment N 5 Yahia El Horbaty, Khouzeima M

Could you please help me in this probability and Stat assignment ?

MACT 3224/317: Assignment N 5

Yahia El Horbaty, Khouzeima Moutanabbir Abd-Elnasser Saad and Noha Youssef ? Fall 2016 Return this page with your signature

? Name:

? Student ID:

? Section number:

I certify that this is my own work, and that I have not copied the work of another student.

? Date:

? Signature:

Please follow the instructions below

? Write your name and section number at the spaces provided.

? Give clear answers and explanations justifying your method wherever possible.

? Due Thursday, December 15, 2016 at 2:00 pm.

? Submit your work to our teaching assistant.

? Homework cannot be submitted as an e-mail attachment.

? Late submissions are not allowed. ? The Department of Mathematics and Actuarial Science, The American University in Cairo. 1 ? Question 1:

An investigator computes a 95% confidence interval for a population mean on the basis of a sample of

size 70. If she wishes to compute a 95% confidence interval that is half as wide, how large a sample

does she need?

? Question 2:

A random sample of the number of barrels (in millions) of oil produced per day by world oil producing

countries is listed here:

3.56 1.90 7.83 2.83 1.91 5.88 2.91 6.08 (a) Find the sample mean and the sample standard deviation.

(b) Estimate the mean oil production per day with 95% confidence.

? Question 3:

An electrical engineer wants to compare the mean melting points for two di?erent metal alloys used

in soldering. He collects a sample of size n1 = 36 for the melting point of alloy 1 and finds a sample

average 185 o C. He collects a sample of size n2 = 64 for melting point of alloy 2 and finds a sample

average of 183 o C. Assume that the population standard deviation for the melting point of the first

alloy is 1 = 3 o C and the population standard deviation for the melting point of the second alloy is

o

2 = 4 C.

(a) Compute a 95% confidence interval for the di?erence of the means ?1

(b) Using a hypothesis test at level 0.05, is there evidence to claim that ?1 ?2 .

?2 = 1o C? ? Question 4:

A sample of 64 resistors are taken from a production line and are found to have a sample mean of

998 Ohms. The population distribution for the resistances is unknown but the population standard

deviation is known to be 10 Ohms.

(a) Find a 98% confidence interval for the population mean.

(b) Answer the following two questions by writing either ?narrower? or ?wider? in the blank space and

justify your answer

1. If the sample size were increased to n = 1000 then the confidence interval would be

the confidence interval computed from a sample with n = 64.

2. A 99% confidence interval is

than a 98% confidence interval. than ? Question 5:

A manufacturer claims that the average life of their electrical light bulbs is 2000 hours. A random

sample of 64 bulbs is tested and the life,x, in hours is recorded. The results obtained are as follows

Pn

?

i=1 xi = 127808

Pn

?

x)2 = 9694.6

i=1 (xi

(a) Is there sufficient evidence, at the 1%, that supports the manufacturer?s claims. (b) Is there sufficient evidence, at the 1%, that the manufacturer overestimates the length of life of

the light bulb.

? Question 6:

In communications let p denote the probability that a bit sent by the transmitter will be received erroneously on the other end of the channel. A telecom company has determined that for a communication

channel an error rate of more than 0.05 is unacceptable. To perform the test, a predetermined 32 bit

long message is sent (this is a sample with n = 32) and the number of erroneous bits are counted at

the receiving end. The number of erroneous bits is 2.

2 (a) Find a 99% confidence interval for the true probability p.

(b) Using a hypothesis test at level 0.01, can we conclude that the data present sufficient evidence to

suggest that the rate p is unacceptable?

? Question 7:

A questionnaire of spending habits was given to a random sample of college students. Each student

was asked to record and report the amount of money they spent on textbooks in a semester. The

sample of 130 students resulted in an average of $422 with standard deviation of $57.

1. Give a 90% confidence interval for the mean amount of money spent by college students on

textbooks.

2. How many students should you sample if you want a margin of error of $5 for a 90% confidence

interval? 3

**Solution details:**

Answered

QUALITY

Approved

ANSWER RATING

This question was answered on: * Sep 18, 2020 *

* * Solution~0001013410.zip (25.37 KB)

This attachment is locked

We have a ready expert answer for this paper which you can use for in-depth understanding, research editing or paraphrasing. You can buy it or order for a fresh, original and plagiarism-free copy from our tutoring website www.aceyourhomework.com (Deadline assured. Flexible pricing. TurnItIn Report provided)

##### Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .

#### About this Question

STATUSAnswered

QUALITYApproved

DATE ANSWEREDSep 18, 2020

EXPERTTutor

ANSWER RATING

#### GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

- As a reference for in-depth understanding of the subject.
- As a source of ideas / reasoning for your own research (if properly referenced)
- For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).

#### NEW ASSIGNMENT HELP?

### Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions.
New orders are original solutions *and precise to your writing instruction requirements. Place a New Order using the button below.*

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN YOUR SET DEADLINE.