1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Scorpion4ik [409]
3 years ago
8

The following results come from two independent random samples taken of two populations.

Mathematics
1 answer:
photoshop1234 [79]3 years ago
8 0

Answer:

(a)\ \bar x_1 - \bar x_2 = 2.0

(b)\ CI =(1.0542,2.9458)

(c)\ CI = (0.8730,2.1270)

Step-by-step explanation:

Given

n_1 = 60     n_2 = 35      

\bar x_1 = 13.6    \bar x_2 = 11.6    

\sigma_1 = 2.1     \sigma_2 = 3

Solving (a): Point estimate of difference of mean

This is calculated as: \bar x_1 - \bar x_2

\bar x_1 - \bar x_2 = 13.6 - 11.6

\bar x_1 - \bar x_2 = 2.0

Solving (b): 90% confidence interval

We have:

c = 90\%

c = 0.90

Confidence level is: 1 - \alpha

1 - \alpha = c

1 - \alpha = 0.90

\alpha = 0.10

Calculate z_{\alpha/2}

z_{\alpha/2} = z_{0.10/2}

z_{\alpha/2} = z_{0.05}

The z score is:

z_{\alpha/2} = z_{0.05} =1.645

The endpoints of the confidence level is:

(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}

2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}

2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}

2.0 \± 1.645 * \sqrt{0.0735+0.2571}

2.0 \± 1.645 * \sqrt{0.3306}

2.0 \± 0.9458

Split

(2.0 - 0.9458) \to (2.0 + 0.9458)

(1.0542) \to (2.9458)

Hence, the 90% confidence interval is:

CI =(1.0542,2.9458)

Solving (c): 95% confidence interval

We have:

c = 95\%

c = 0.95

Confidence level is: 1 - \alpha

1 - \alpha = c

1 - \alpha = 0.95

\alpha = 0.05

Calculate z_{\alpha/2}

z_{\alpha/2} = z_{0.05/2}

z_{\alpha/2} = z_{0.025}

The z score is:

z_{\alpha/2} = z_{0.025} =1.96

The endpoints of the confidence level is:

(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}

2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}

2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}

2.0 \± 1.96 * \sqrt{0.0735+0.2571}

2.0 \± 1.96* \sqrt{0.3306}

2.0 \± 1.1270

Split

(2.0 - 1.1270) \to (2.0 + 1.1270)

(0.8730) \to (2.1270)

Hence, the 95% confidence interval is:

CI = (0.8730,2.1270)

You might be interested in
Terms that have the same variables raised to the same powers are called ___ terms.
Gnom [1K]
The answer is like terms.
6 0
3 years ago
How long does it take for a bee to fly 12 miles going 15 mph?
sladkih [1.3K]
Two hours ! i think i'm not good at many
4 0
3 years ago
Check image please help
Stells [14]

Answer:

Step-by-step explanation:

"The total number of dollars in fives and tens" tells you that these denominations are being added together.  Because a five dollar bill is worth $5 and a ten dollar bill is worth $10, then the number of $5 bills is represented by 5f and a the number of $10 bills is represented by 10t.  Therefore,

T = 5f + 10t

3 0
3 years ago
what’s the difference between the area of the larger circle and the area of the smaller circle? in pi
Arisa [49]

Answer:

105 pi m^2

Step-by-step explanation:

radius squared - radius squared =

(16+3)^2 - 16^2 =

19^2 - 16^2 =

361-256= 105

7 0
3 years ago
What is the place value of the 2 in 6,025
Ray Of Light [21]

Answer: tens


Step-by-step explanation: the number 2 is in the tens place because 6,025= 6 is in the thousands place 0 is in the hundredths place 2 is in the tens place and 5 is in the ones place

PLEASE MARK BRAINLIEST


8 0
3 years ago
Other questions:
  • Graph a line with a slope of -3 and a y-intercept of 4
    13·1 answer
  • How do I write 770,070 in expanded form
    8·1 answer
  • Jane bought a packet of 12 cards for $15.00 <br>What would be the average price of a card?
    14·2 answers
  • The width of a rectangle is equal to m cm, but its length is five times greater than the width. Find the area of the rectangle
    7·1 answer
  • What’s the answer/ how should I work it?
    8·1 answer
  • In a test containing 10 questions, (+5) marks are awarded for every correct answer, (-1) mark for every incorrect answer and 0 f
    8·1 answer
  • I was wondering if anyone could answer this :)
    13·2 answers
  • Exterior Angle Theorem
    9·1 answer
  • 34.75 divided by 5 equals what
    7·2 answers
  • A relatively prime date is a date for which the number of the month and the number of the day are relatively prime. For example,
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!