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
alex41 [277]
3 years ago
9

In 2003, the Accreditation Council for Graduate Medical Education (ACGME) implemented new rules limiting work hours for all resi

dents. A key component of these rules is that residents should work no more than 80 hours per week. The following is the number of weekly hours worked in 2016 by a sample of residents at the Tidelands Medical Center. 78 85 82 79 77 82 81 82 81 81 82 78
a. What is the point estimate of the population mean?
b. Develop a 99% confidence interval for the population mean.
c. Is the company’s claim that the "typical customer" spends $80 per month reasonable? Yes/No
Mathematics
1 answer:
Ainat [17]3 years ago
3 0

Answer:

a) \bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

The mean calculated for this case is \bar X=80.67

b) The sample deviation calculated s=2.270

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

df=n-1=12-1=11

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(0.005,11)".And we see that t_{\alpha/2}=3.106

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

80.67-3.106\frac{2.270}{\sqrt{12}}=78.635    

80.67+3.106\frac{2.270}{\sqrt{12}}=82.705    

So on this case the 99% confidence interval would be given by (78.635;82.705)    

c) Yes since the confidence interval calculated include the value of 80 for a possible value for the true mean of interest

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 represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Part a

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 mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=80.67

Part b

The sample deviation calculated s=2.270

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

df=n-1=12-1=11

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(0.005,11)".And we see that t_{\alpha/2}=3.106

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

80.67-3.106\frac{2.270}{\sqrt{12}}=78.635    

80.67+3.106\frac{2.270}{\sqrt{12}}=82.705    

So on this case the 99% confidence interval would be given by (78.635;82.705)    

Part c

Yes since the confidence interval calculated include the value of 80 for a possible value for the true mean of interest

You might be interested in
Hi I hope you can help me im struggling with this. ((: I'll give you a brainy thing if your right​
Serggg [28]
It’s d because 15 more than 6 times a number would be 15+6x if that makes sense
6 0
3 years ago
Enter the value of 12x-2 when x = 3.
alina1380 [7]

Answer:

34

Step-by-step explanation:

12(3)-2

36-2

34

3 0
2 years ago
Read 2 more answers
Need Help on this problem
natta225 [31]

Answer:3808

Step-by-step explanation: 17x16x14

4 0
3 years ago
Can someone plz help Me?
hammer [34]

Answer:

A

^{}

3 0
2 years ago
Read 2 more answers
What is the total value of the digit 4 in the number: 34,712?<br> 40<br> 1,000<br> 400<br> 4,000
aev [14]

Answer: 4,000

Step-by-step explanation:

It is in the thousands place

4 0
2 years ago
Other questions:
  • Factor the expression completely <br> 8y-36
    13·1 answer
  • Is x+1 a factor? Why or why not?
    13·1 answer
  • If f(x)=3^x+10x and g(x)=4x-2 find (f+g)(x)
    6·1 answer
  • Find the missing length
    5·1 answer
  • Dominic uses 1/2 tablespoon of almond butter to make a sandwich he needs to make five sandwiches how many tablespoons of almond
    6·1 answer
  • How can x2+3x+1=2x2+2x+3 be set up as a system of equations
    10·1 answer
  • What is the maximum slope to f(x)= e^(-x^2)?
    10·1 answer
  • Which of the following terms correctly describe the object below?
    12·1 answer
  • -<br> Factor Completely : 6w2 – 66w – 72
    8·2 answers
  • 13. 92÷3 need to know estimation and show work
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!