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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   )

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Answer:

715 pounds

Step-by-step explanation:

<em>FV = solve</em>

<em>PV = 600</em>

<em>I% = 6</em>

<em>K = 1, N = 3 </em>(2013 - 2016 = 3 years)

Plug it in:

<em>FV = 600 x [ 1 + (6/100 x 1)]³</em>

= 600 x ( 1 + 0.06)³

= 600 x (1.06)³

FV = 714.61, 715 to the nearest dollar.

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3 years ago
A rental car agency charges a flat fee of $139.00 plus $30.00 per day to rent a certain car. Another agency charges a fee of $13
Sveta_85 [38]
139 + 30d = 13 + 51d
139 - 13 = 51d - 30d
126 = 21d
126/21 = d
6 = d

now lets check..
139 + 30d = 139 + 30(6) = 319
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5 0
3 years ago
The figure below is a regular octagon with a side length of 8 inches.
Masteriza [31]

Answer:

309in²

Step-by-step explanation:

Area of an octagon is expressed as;

A=2(1+√2)a²

a is the side length of the octagon

Given

a = 8

Substitute into the formula

A = 2(1+√2)(8)²

A = 2(1+√2)(64)

Expand

A = 2(64+64√2)

A = 128+128√2

A = 128+128(1.414)

A = 128+181.01

A = 309in²

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Calculati:
kramer

Answer:

7

Step-by-step explanation:

[(1/3 – 1/9)² + (1/3)³] : (1/3)⁴

Next, we shall simplify (1/3 – 1/9)². This is illustrated below:

(1/3 – 1/9)² = ((3 – 1)/9)² = (2/9)²

[(1/3 – 1/9)² + (1/3)³] : (1/3)⁴

= [(2/9)² + (1/3)³] : (1/3)⁴

= [4/81 + 1/27] : 1/81

= [(4 + 3)/81 ] : 1/81

= 7/81 : 1/81

= 7/81 ÷ 1/81

Invert

= 7/81 × 81/1

= 7

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