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
Leni [432]
3 years ago
14

A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. U

sing this data to obtain a 95 percent confidence interval resulted in an interval from 47.19 to 52.61. True or False: The confidence interval obtained is valid only if the distribution of the population of salary offers is normal.
Mathematics
1 answer:
balu736 [363]3 years ago
6 0

Answer:

Step-by-step explanation:

number of samples, n = 10

Mean = (48 + 51 + 46 + 52 + 47 + 48 + 47 + 50 + 51 + 59)/10 = 49.9

Standard deviation = √(summation(x - mean)/n

Summation(x - mean) = (48 - 49.9)^2 + (51 - 49.9)^2 + (46 - 49.9)^2+ (52 - 49.9)^2 + (47 - 49.9)^2 + (48 - 49.9)^2 + (47 - 49.9)^2 + (50 - 49.9)^2 + (51 - 49.9)^2 + (59- 49.9)^2 = 128.9

Standard deviation = √128.9/10 = 3.59

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 10 - 1 = 9

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.262

Margin of error = 2.262 × 3.59/√10

= 2.57

the lower limit of this confidence interval is

49.9 - 2.57 = 47.33

the lower limit of this confidence interval is

49.9 + 2.57 = 52.47

So it is false

You might be interested in
Multiplying and Dividing Integers<br><br> (-8) x (-6) =
snow_tiger [21]

Answer:

Positive 48 or 48

Step-by-step explanation: When we multiply a negative by a negative, it ends up being a positive. -8 x -6=48

4 0
3 years ago
Please answer number one as well as show your work thank you!
sveta [45]

√2 is irrational

a rational number Q can be expressed in the form \frac{a}{b} where a and b are integers.

- 18 = \frac{- 18}{1} ⇒ rational

\frac{2}{3} ⇒ rational

3.14 = \frac{314}{100} ⇒ rational

√2 = 1.414213562...... ⇒ irrational


8 0
3 years ago
16. Solve 7n=42<br> 06<br> O n = 6<br> n = 7<br> O 7
Masteriza [31]

Answer:

6

Step-by-step explanation:

7n=42

n=42/7

n=6

7 0
2 years ago
4 Find a formula for the exponential function passing through the points (-2, 4/9) and (3, 108)​
NemiM [27]

9514 1404 393

Answer:

  f(x) = 4·3^x

Step-by-step explanation:

We assume the function will be of the form ...

  f(x) = a·b^x

Substituting the given values, we can find 'a' and 'b'.

  4/9 = a·b^(-2)

  108 = a·b^3

Dividing the second equation by the first gives ...

  108/(4/9) = b^(3 -(-2))

  243 = b^5

  b = 3 . . . . . . 5th root

Using the second equation, we can find 'a':

  108 = a·3^3 = 27a

  a = 108/27 = 4

The formula for the exponential function is ...

  f(x) = 4·3^x

3 0
3 years ago
Name 3 reasons why explorers made their difficult and dangerous trips.
dybincka [34]
~To explore/find new lands
~To discover new goods
~To trade or sell
6 0
3 years ago
Other questions:
  • The figure below shows segments PQ and RS which intersect at point t. Segment PR is parallel to segment SQ.
    11·1 answer
  • The ratio of the length of a rectangular field to its width is 4:3. If the length of the field is 100 meters, what is the perime
    14·1 answer
  • Melinda and Marcus are saving money to purchase a present for a friend. Each friend starts with an amount and also saves a speci
    6·2 answers
  • Helena makes an 8% commission on any artwork she sells. If she sells $125 worth of artwork, how much is her commission.
    15·1 answer
  • Please help, On Saturday morning, Owen earned $21. By the end of the afternoon he had earned a total of $60. Enter an equation,
    11·1 answer
  • Due today please help!<br> Need help with 9 and 10! Will give a lot of points and brainliest!
    11·1 answer
  • Find the value of x. 8,13,x
    6·1 answer
  • Why do you think a quadratic always becomes a positive number?
    13·1 answer
  • Which statement is true?<br> A<br> 0.265 &lt;0.3<br> B<br> 0.265 &gt;0.3<br> C<br> 0.265 =0.3
    9·1 answer
  • A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!