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
slava [35]
3 years ago
12

The amount of money spent on textbooks per year for students is approximately normal.

Mathematics
1 answer:
Contact [7]3 years ago
8 0

Answer:

(A) A 95% confidence for the population mean is [$332.16, $447.84] .

(B) If the confidence level in part (a) changed from 95% to 99%, then the margin of error for the confidence interval would increase.

(C) If the sample size in part (a) changed from 19 to 22, then the margin of error for the confidence interval would decrease.

(D) A 99% confidence interval for the proportion of students who purchase used textbooks is [0.363, 0.477]  .

Step-by-step explanation:

We are given that 19 students are randomly selected the sample mean was $390 and the standard deviation was $120.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean = $390

            s = sample standard deviation = $120

            n = sample of students = 19

            \mu = population mean

<em>Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation. </em>

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ; </u>

P(-2.101 < t_1_8 < 2.101) = 0.95  {As the critical value of t at 18 degrees of

                                               freedom are -2.101 & 2.101 with P = 2.5%}  

P(-2.101 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.101) = 0.95

P( -2.101 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.101 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-2.101 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.101 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u> 95% confidence interval for</u> \mu = [ \bar X-2.101 \times {\frac{s}{\sqrt{n} } } , \bar X+2.101 \times {\frac{s}{\sqrt{n} } } ]

                        = [ \$390-2.101 \times {\frac{\$120}{\sqrt{19} } } , \$390+2.101 \times {\frac{\$120}{\sqrt{19} } } ]

                        = [$332.16, $447.84]

(A)  Therefore, a 95% confidence for the population mean is [$332.16, $447.84] .

(B) If the confidence level in part (a) changed from 95% to 99%, then the margin of error for the confidence interval which is Z_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} } would increase because of an increase in the z value.

(C) If the sample size in part (a) changed from 19 to 22, then the margin of error for the confidence interval which is Z_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} }  would decrease because as denominator increases; the whole fraction decreases.

(D) We are given that to estimate the proportion of students who purchase their textbooks used, 500 students were sampled. 210 of these students purchased used textbooks.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                             P.Q.  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion students who purchase their used textbooks = \frac{210}{500} = 0.42    

            n = sample of students = 500

            p = population proportion

<em>Here for constructing a 99% confidence interval we have used a One-sample z-test statistics for proportions</em>

<u>So, 99% confidence interval for the population proportion, p is ; </u>

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5%

                                               level of significance are -2.58 & 2.58}  

P(-2.58 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 2.58) = 0.99

P( -2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

P( \hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

<u> 99% confidence interval for</u> p = [ \hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ]

= [ 0.42 -2.58 \times {\sqrt{\frac{0.42(1-0.42)}{500} } } , 0.42 +2.58 \times {\sqrt{\frac{0.42(1-0.42)}{500} } } ]

= [0.363, 0.477]

Therefore, a 99% confidence interval for the proportion of students who purchase used textbooks is [0.363, 0.477]  .

You might be interested in
You got two questions wrong on your ten question quiz. What percent did you earn in the grade-book?
hjlf

Answer:

80% that is what you got is this a test question  or no?

Step-by-step explanation:


4 0
3 years ago
Read 2 more answers
The circumference of a circle
Dmitry_Shevchenko [17]
Use the formula C = pi * d
8 0
3 years ago
Solve the system:<br> 4x – 3y = -21<br> X=-y-14
Liula [17]

Answer:

The solution for the system of equations is

x=2,y=−2

Explanation:

4x−3y=14.....equation (1)

y=−3x+4.....equation (2)

Solving by substitution

Substituting equation 2 in equation 1

4x−3⋅(−3x+4)=14

4x+9x−12=14

13x=14+12

13x=26

x=2

Finding y by substituting x in equation 1

4x−3y=14

4⋅2−3y=14

8−3y=14

8−14=3y

3y=−6

y=−2

4 0
3 years ago
Read 2 more answers
I need an answer ASAP pls
tino4ka555 [31]

Answer:

Age 42 salary 30,000

Step-by-step explanation:

He had to restart his medical training, therefore, making him have a lower salary regardless of his age, making this point an obvious outlier

4 0
3 years ago
Jill wants to make 15 no of a 40% acid solution by mixing together a 30% acid solution and a 60% acid solution. How much of each
german
X+y=15
0.3x+0.6y=0.4*15=6
solve the system of equation.
Multiply equation one by 0.3: 0.3x+0.3y=4.5
subtract the new from the second equation: 0.3y=1.5
y=5
x=10 
7 0
3 years ago
Read 2 more answers
Other questions:
  • 9. If a car travels 65 kilometers in 25 minutes, what is its speed in miles per hour? (1.6 km = 1 mile)
    15·1 answer
  • Employees at a company are given a three digit employee identification code. If each digit cannot be repeated, how many differen
    9·1 answer
  • An + bn HELLLP WHAT IS THIS ANSWER
    7·1 answer
  • A scale drawing of a bathroom is shown:
    11·1 answer
  • How many square feet of outdoor carpet will we need for this hole? Help asap
    6·1 answer
  • What is the missing length?
    10·1 answer
  • Find the value of X????
    13·2 answers
  • NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.
    9·1 answer
  • Find the area of the triangle. Round to the nearest<br> tenth.
    15·1 answer
  • For right triangle ABC, find the sine ratio of angle θ.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!