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
Step2247 [10]
3 years ago
12

If Upper X overbar equals 62​, Upper S equals 8​, and n equals 36​, and assuming that the population is normally​ distributed, c

onstruct a 99 % confidence interval estimate of the population​ mean, mu.
Mathematics
1 answer:
marishachu [46]3 years ago
3 0

Answer:

The 99% confidence interval would be given by (58.373;65.627)    

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=62 represent the sample mean

\mu population mean (variable of interest)

s=8 represent the sample standard deviation

n=36 represent the sample size  

Part a: Confidence interval

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=36-1=35

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,35)".And we see that t_{\alpha/2}=2.72

Now we have everything in order to replace into formula (1):

62-2.72\frac{8}{\sqrt{36}}=58.373    

62+2.72\frac{8}{\sqrt{36}}=65.627    

So on this case the 99% confidence interval would be given by (58.373;65.627)    

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

You might be interested in
302 car stereos were recently sold in a car audio store. 149 had a CD player, 116 had a cassette player, and 40 had both a CD an
Mandarinka [93]

Answer:

109 car stereos

Step-by-step explanation:

If 149 car stereos had a CD player (with or without a cassette player), and 40 car stereos had both a CD and a cassette player, the number of stereos with only a CD player is determined by:

CD_{only} = CD - Both\\CD_{only} =149-40\\CD_{only} =109\ car\ stereos

109 car stereos had only a CD player.

4 0
3 years ago
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
kompoz [17]

Answer:

d<u>></u>-7

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What's the points distance I need help!​
KATRIN_1 [288]

Answer:

Step-by-step explanation:

3.6

6 0
2 years ago
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Reptile [31]

Step-by-step explanation:

18% compounded monthly

vs

charges 18% compounded semi-annually.

#1 is worse than #2 because...

Since the nominal rates are the same, the card with the more frequent compounding so it would have the higher effective rat.

Let's compare them!:

(1 + .18/12)^12 = 1.19562 ---> effective rate is 19.562 per annum

(1+.18/2)² = 1.1881

1.1881 has the effective rate of 18.88% per annum

(1 + /17/4)^4 = 1.18114.. --> effective rate is 18.114% per annum

18% monthly is .18 over 12 each month = 0.015/month

so every month multiply by 1.015

total cost = $607.99 * 1.01^number of months

18% semi annual = .18/2 every six months = .09 /half year

so every half year (6 months) multiply by 1.09

total cost = $607.99 * 1.09^ (number of months/6)

17% quarterly = .17/4 every 3 months = .0425 /quarter year

so every quarter year (3 months) multiply by 1.0425

total cost = $607.99 * 1.025^(number of months/3)

HOPE THIS HELPS YOU HAVE A GREAT GREAT GREAT FANTASTIC FRIDAY!

7 0
3 years ago
What is the quotient
taurus [48]

The second one: 4 times 10 to the power of 12

5 0
3 years ago
Read 2 more answers
Other questions:
  • A company designed a cheese container in the shape of a triangular pyramid. The base of the pyramid must have an are of 81 squar
    9·1 answer
  • A new law has support from some Democrats and some Republicans. The table shows the relative frequencies of the columns for the
    14·2 answers
  • 5(x-10)=30-15x<br> Ox=1<br> Ox=4<br> Ox=5<br> Ox=8
    12·1 answer
  • Sam plays a game using a spinner like the one below which event or complement has a probability of 3/4
    9·1 answer
  • A chemist is conducting an experiment which involves a certain chemical reaction. He begins the experiment with 824 milliliters
    9·1 answer
  • mondays high temperature was 6 degrees celcius. the low temperture was -3 degrees celcius. what was the difference between the h
    5·2 answers
  • Order each set of values from least to greatest 0.4 and 5/8 and 38%
    8·2 answers
  • Simplify 5 over -32 squared simplified
    5·2 answers
  • HELP PLZ!!!!!!!!!!!!!!!
    10·2 answers
  • P(x)= 2x^3-x^2+5 is divided by x+2. Choose the correct option from drop menu.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!