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3 years ago

Harry purchased 16 hinges for his kitchen project. They were each on sale for $3 off the regular price.

Mathematics

2 answers:

Lunna [17]3 years ago

7 0

80/16=5 since they were $3 off the regular price is 8

Marysya12 [62]3 years ago

5 0

First divide 80 by 16: 80/16=5

Since they say the original price was $3 more than when the sale came you have to do 5+3=8

$8 is the original price of each hinge

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4 years ago

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3 years ago

Read 2 more answers

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the f

Verizon [17]

Answer:

CI(95%): [205,5;400.8]dolars

Step-by-step explanation:

Hello!

So you need to construct a confidence interval for the average family dental expenses (μ) using the sample given in the problem. To estimate it you need to first choose a statistic. For this small sample, considering that the variable has a normal distribution (I made a quick Shapiro Wilks test, with p-value 0.3234, you can assume normality) the best statistic to use is the Student's t-test.

t= [x(bar)-μ]/S/√n ≈ t₍ₙ₋₁₎

The formula for the confidence interval to estimate the mean is

x(bar)± $t_{n-1; 1-\alpha/2}$ * (S/√n)

The critical value is from a t-distribution with 11 degrees of freedom

± $t_{n-1; 1-\alpha/2} = t_{11; 0.975} = 2.201$

>remember since it's two-tailed, to get the right critical value you have to divide α by 2. So in the text, you received a confidence level of 1-α=0.95 so α=0.05 then α/2=0.025 and 1-α/2=0.975

To construct the interval, you need to first calculate the sample mean and the standard derivation.

Sample

115; 370; 250; 593; 540; 225; 117; 425; 318; 182; 275; 228

n= 12

∑xi = 3638 ∑xi² = 1362670

Sample mean

x(bar): (∑xi)/n = 3638/12 = 303.17 dolars

Standard derivation

S²= 1/n-1*[∑xi²- (∑xi)²/n] = 1/11 * [1362670-((3638)²/12)] = 23614.47 dolars²

S= 153.67 dolars

Confidence interval (95%)

303.17± 2.201* (153.67/√12)

[205,5;400.8]dolars

I hope you have a SUPER day!

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