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
ryzh [129]
3 years ago
14

he owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on w

eekdays and weekends. The owner samples 5 weekdays and finds an average of 259.23 gallons of milk sold on those days with a standard deviation of 34.713. 10 (total) Saturdays and Sundays are sampled and the average number of gallons sold is 365.12 with a standard deviation of 48.297. Construct a 90% confidence interval to estimate the difference of (average number of gallons sold on weekdays - average number of gallons sold on weekends). Assume the population standard deviations are the same for both weekdays and weekends.
Mathematics
1 answer:
stellarik [79]3 years ago
3 0

Answer:

90% confidence interval is ( -149.114, -62.666   )

Step-by-step explanation:

Given the data in the question;

Sample 1                                Sample 2

x"₁ = 259.23                            x"₂ = 365.12

s₁  = 34.713                              s₂ = 48.297

n₁ = 5                                       n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

S_p^2 = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

S_p^2 = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

S_p^2 = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [  4 + 9 ]

S_p^2 = [ 4819.9692 + 20993.4 ] / [  13 ]

S_p^2 = 25813.3692 / 13

S_p^2 = 1985.64378

Now the Standard Error will be;

S_{x1-x2 = √[ ( S_p^2 / n₁ ) + ( S_p^2 / n₂ ) ]

we substitute

S_{x1-x2 = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

S_{x1-x2 = √[ 397.128756 + 198.564378 ]

S_{x1-x2 = √595.693134

S_{x1-x2 = 24.4068

Critical Value = t_{\frac{\alpha }{2}, df = t_{0.05, df=13 = 1.771  { t-table }

So,

Margin of Error E =  t_{\frac{\alpha }{2}, df × [ ( S_p^2 / n₁ ) + ( S_p^2 / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666   )

You might be interested in
A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red
mamaluj [8]

Let red marbles = X.

The probability is 1 out of 5, written as 1/5

1/5 in terms of red marbles is equal to the number of red marbles divided by 5x, where 5x is the total number of marbles.

1/5 = x/5x 

Now you have 5x total marbles, x red and 4x blue. 

Add 5 more red and the new probability is: 

(x+5)/(5x+5) = 1/3 

Simplify:

3x+15 = 5x+5 

Now solve for x:

Subtract 3x from both sides:

15 = 2x +5

Subtract 5 from each side:

2x = 10 

Divide both sides by 2:

x = 10/2

X = 5

There were originally 5 red marbles.

5 0
3 years ago
Is $5.40 the same as $7.00?
natita [175]

Answer:

5.40 is not the same as 7.00

Step-by-step explanation:

6 0
3 years ago
How can I simplify/rewrite the 1st(top) equation into the 2nd(Botton),please show a step by step solution.​
Vaselesa [24]

Answer:

see below

Step-by-step explanation:

-2(4 - \frac{x}{2} )^{5} + C

Think of the above as:

  -\frac{2}{1} * (\frac{8}{2} - \frac{x}{2} )^{5} + C

= -\frac{2}{1} * \frac{(8 - x)^{5}}{2^{5}}  + C

= -\frac{2}{1} * \frac{(8 - x)^{5}}{32}  + C

= -\frac{1}{1} * \frac{(8 - x)^{5}}{16}  + C

=   \frac{-1(8 - x)^{5}}{16}  + C

=   \frac{(-8 + x)^{5}}{16}  + C

Can flip it around to be...

\frac{(x - 8)^{5}}{16}  + C

4 0
3 years ago
The greatest comen factor of 24 and 30
Alja [10]

Answer:

6

Step-by-step explanation:

Write the prime factorizations:

24 = 2³ × 3

30 = 2 × 3 × 5

The greatest common factor is the product of the common factors at their lowest exponents.

GCF = 2 × 3

GCF = 6

7 0
3 years ago
Read 2 more answers
Your class is having a pizza party. You buy 5 pizzas Each pizz has 4 slices. How many slices is that altogether?​
bixtya [17]

Answer:

20

Step-by-step explanation:

5 x 4 = 20

3 0
2 years ago
Read 2 more answers
Other questions:
  • A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. if the machine has a standard deviation in del
    12·1 answer
  • Can anyone help? Thank you.
    11·1 answer
  • What is 5% as a fraction in simplest form
    8·1 answer
  • The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x)=2x^
    9·1 answer
  • Please help! Will give brainliest!<br><br> Option choices are 2, -5. 11
    13·1 answer
  • Make a frequency table and a dot plot for the Korean class
    13·1 answer
  • . I. The graphs of all linear relationships are a line.
    13·1 answer
  • Log10 (x squared - 4x + 7) = 2
    11·1 answer
  • Please help me big finals test!!!!
    10·1 answer
  • Which table of ordered pairs represents a linear function? x y −8 22 0 1 8 22 16 102 x y −8 −7 0 1 8 9 8 2 x y −8 −7 0 0 8 7 16
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!