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mezya [45]
2 years ago
14

A consumer agency is interested in examining whether there is a difference in two common sealant products used to waterproof res

idential backyard decks. With cooperation of several builders in the area, they randomly assign 38 newly constructed decks to be treated with Very Clear deck sealant and another 37 newly constructed decks to be treated with Sure Seal deck sealant. After one year of being exposed to similar weather conditions, the decks are rated on a scale of 1 to 100. The mean rating for the decks treated with Very Clear is 89.2 with a standard deviation of 3.1. The mean rating for the decks treated with Sure Seal is 92.4 with a standard deviation of 3.8.
Required:
What represents the 90 percent confidence interval to estimate the difference (Very Clear minus Sure Seal) in mean ratings for the two deck sealants?
Mathematics
1 answer:
spin [16.1K]2 years ago
3 0

Answer:

(89.2 - 92.4) ± 1.666*√(3.1²/38 + 3.8²/37)

Step-by-step explanation:

Very clear deck :

n1 = 38

x1 = 89.2

s1 = 3.1

Sure seal

n2 = 37

x2 = 92.4

s2 = 3.8

Confidence interval for difference in sample means :

(X1 - X2) ± margin of error

(X1 - X2) ± Tcritical * sqrt(s1²/n1 + s2²/n2))

Using the degree of freedom calculator ; df = 70

Margin of Error : Tcritical * sqrt(s1²/n1 + s2²/n2))

Tcritical at 90% confidence interval, df = 70 = 1.688

Margin of Error = 1.666 * sqrt(3.1²/38 + 3.8²/37)

Confidence interval :

(89.2 - 92.4) ± 1.666*√(3.1²/38 + 3.8²/37)

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7 0
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The sum of 5 consecutive even numbers is 20
vladimir2022 [97]

Step-by-step explanation:

Let the 1st number be x

2nd number = x + 2

3rd number = x + 4

4th number = x + 6

5th number = x + 8

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The 5 consecutive integers are

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8 0
3 years ago
Pls do it for me thank you so much
Bond [772]

Answer:

(a) Attached to this response.

(b)

<em>(i)</em> <em>0 cups = 0.275</em>

<em>(ii) 4 cups = 0.125</em>

<em>(iii) 8 cups = 0.025</em>

<em />

<em />

Step-by-step explanation:

(a) The frequency and relative frequency table has been attached to this response.

i. The first column, labelled x, is the number of cups of coffee consumed per day.

ii. The second column, labelled f, is the number of people that consumed x cups of coffee per day. It is found by counting the number of occurrences (i.e frequency) of the numbers of the first column, x, in the given data.

For example, 0 in first column appears 11 times in the given data. Also, 5 in the first column appears 4 times in the given data.

iii. The third column, labelled r, is the relative relative frequency of the number of cups of coffee. It is calculated by dividing the frequency of the cups of coffee by the total number of people that consumed it. As shown on the table, it is calculated by dividing the each of the values on the second column by the sum of the values on that same column (second column).

For example, the relative frequency of 2 cups of coffee is given by:

r = 7  ÷ 40 = 0.175

Also, the relative frequency of 4 cups of coffee is given by;

r = 5 ÷ 40 = 0.125

(b) The probability (Pₓ) that a randomly selected person consumed x cups of coffee is given by;

Pₓ = frequency of x ÷ total frequency

This is also the relative frequency of x

Therefore,

<em>(i) The probability (P₀) that a randomly selected person consumed 0 cups of coffee is given by;</em>

the relative frequency of 0<em> = 0.275</em>

<em></em>

<em>(ii) The probability (P₄) that a randomly selected person consumed 4 cups of coffee is given by;</em>

the relative frequency of 4<em> = 0.125</em>

<em>(iii) The probability (P₈) that a randomly selected person consumed 8 cups of coffee is given by;</em>

the relative frequency of 8<em> = 0.025</em>

<em></em>

<em></em>

<em></em>

Download docx
5 0
3 years ago
My small brain is collapsing because of this question please help
Viktor [21]

Answer:

  • Option A

Step-by-step explanation:

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  • - 3 > 4, incorrect as - 3 is to the left of 4
  • - 2 < - 3, incorrect as - 3 is to the left of - 2
  • - 3 < - 6, incorrect as - 6 is to the left of - 3
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2 years ago
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