Mathematics High School

Construct a 90% confidence interval for μ1-μ2 with the sample statistics for mean calorie content of two​ bakeries' specialty pies and confidence interval construction formula below. Assume the populations are approximately normal with equal variances.

Construct A 90% Confidence Interval For 1-2 With The Sample Statistics For Mean Calorie Content Of Two

Answers

Answer 1

Answer:

The 90% confidence interval for the difference in mean (μ₁ - μ₂) for the two bakeries is; (49) < μ₁ - μ₂ < (289)

Step-by-step explanation:

The given data are;

Bakery A

[tex]\overline x_1[/tex] = 1,880 cal

s₁ = 148 cal

n₁ = 10

Bakery B

[tex]\overline x_2[/tex] = 1,711 cal

s₂ = 192 cal

n₂ = 10

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) - t_{c}\cdot \hat \sigma \sqrt{\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}}}< \mu _{1}-\mu _{2}< \left (\bar{x}_1-\bar{x}_{2} \right ) + t_{c}\cdot \hat \sigma \sqrt{\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}}}[/tex]

df = n₁ + n₂ - 2

∴ df = 10 + 18 - 2 = 26

From the t-table, we have, for two tails, [tex]t_c[/tex] = 1.706

[tex]\hat{\sigma} =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]

[tex]\hat{\sigma} =\sqrt{\dfrac{\left ( 10-1 \right )\cdot 148^{2} +\left ( 18-1 \right )\cdot 192^{2}}{10+18-2}}= 178.004321469[/tex]

[tex]\hat \sigma[/tex] ≈ 178

Therefore, we get;

[tex]\left (1,880-1,711 \right ) - 1.706\times178 \sqrt{\dfrac{1}{10}+\dfrac{1}{18}}< \mu _{1}-\mu _{2}< \left (1,880-1,711 \right ) + 1.706\times178 \sqrt{\dfrac{1}{10}+\dfrac{1}{18}}[/tex]

Which gives;

[tex]169 - \dfrac{75917\cdot \sqrt{35} }{3,750} < \mu _{1}-\mu _{2}< 169 + \dfrac{75917\cdot \sqrt{35} }{3,750}[/tex]

Therefore, by rounding to the nearest integer, we have;

The 90% C.I. ≈ 49 < μ₁ - μ₂ < 289

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Answer:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Step-by-step explanation:

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B.
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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

let that number x

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

5.42

Step-by-step explanation:

8.82 -3.4 = 5.42

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2
3
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Answers

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Step-by-step explanation:

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Answers

Answer:

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Answers

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

...........................

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Answers

Answer:

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Step-by-step explanation:

(18u^2 - 142u - 11) ÷ (u - 8)​

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(18u^2 - 142u - 11) ÷ (u - 8)

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Answers

Answer:

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

7x+5y+x+x+x+x

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Answers

Answer:

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Step-by-step explanation:

:)

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

I'm so sorry!!

Answer:

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Answers

105 squared meters is the answer.
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