A line passes through (−1, 5) and (1, 3)

Construct a 99% confidence interval for the population mean, mu. Assume the population has a normal distribution. A group of 1

Zarrin [17]

Answer:

99% confidence interval for the population mean is [19.891 , 24.909].

Step-by-step explanation:

We are given that a group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 99% 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 age of selected students = 22.4 years

s = sample standard deviation = 3.8 years

n = sample of students = 19

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.878 < $t_1_8$ < 2.878) = 0.99 {As the critical value of t at 18 degree of

freedom are -2.878 & 2.878 with P = 0.5%}

P(-2.878 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.878) = 0.99

P( $-2.878 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.878 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ]

= [ $22.4 -2.878 \times {\frac{3.8}{\sqrt{19} }$ , $22.4 +2.878 \times {\frac{3.8}{\sqrt{19} }$ ]

= [19.891 , 24.909]

Therefore, 99% confidence interval for the population mean is [19.891 , 24.909].

6 0

3 years ago

Write down the value of 2 with the power of 3

beks73 [17]

Answer:8

Step-by-step explanation:2 x 2=4 x 2=8

6 0

3 years ago

Read 2 more answers

Complete the steps to add 3 2/5 +1 3/10 . 1. Write mixed numbers as improper fractions. 2. Write equivalent fractions with a com

ira [324]

Answer:

47/10 = 4 7/10

Step-by-step explanation:

3 2/5 + 1 3/10

1. Write mixed numbers as improper fractions:

17/5 + 13/10

2. Write equivalent fractions with a common denominator:

34/10 + 13/10

3. Add the numerators over the common denominator.

47/10

4. Simplify.

4 7/10

3 0

3 years ago

Read 2 more answers

For thousand 400 is 10 times as much as 440

ss7ja [257]

440 x 10 = 4,400. Yes 4,400 is 10 times as much as 440

3 0

3 years ago

Read 2 more answers

Solve for x. enter your answer in interval notation using grouping symbols. x^2+15x<-36

Oliga [24]

X²+15x+36<0

at first solve quadratic equation

D=b²-4ac= 225-4*1*36= 81

x=(-b+/-√D)/2a
x=(-15+/-√81)/2= (-15+/-9)/2
x1=(-15-9)/2=-12
x2=(-15+9)/2=-3

we can write x²+15x+36<0 as (x+12)(x+3)<0

(x+12)(x+3)<0 can be 2 cases, because for product to be negative one factor should be negative , and second factor should be positive
1 case) x+12<0, and x+3>0,
x<-12, and x>-3
(-∞, -12) and(-3,∞) gives empty set

or second case) x+12>0 and x+3<0
x>-12 and x<-3
(-12,∞) and (-∞,-3) they are crossing , so (-12, -3) is a solution of this inequality

3 0

3 years ago