Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for itself since the time it takes to produce the product using the new machine is significantly less than the production time using the old machine. To test the claim, independent random samples were taken from both machines. You are given the following results.New Machine Old Machine
Sample Mean 25 23
Sample Variance 27 7.56
Sample Size 45 36
As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain.

Answers

Answer 1

Answer:

Answer:

z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine

Step-by-step explanation:

We must evaluate the differences of the means of the two machines, to do so, we will assume a CI of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).

New machine

Sample mean x₁ = 25

Sample variance s₁ = 27

Sample size n₁ = 45

Old machine

Sample mean x₂ = 23

Sample variance s₂ = 7,56

Sample size n₂ = 36

Test Hypothesis:

Null hypothesis H₀ x₂ - x₁ = d = 0

Alternative hypothesis Hₐ x₂ - x₁ < 0

CI = 90 % ⇒ α = 10 % α = 0,1 z(c) = - 1,28

To calculate z(s)

z(s) = ( x₂ - x₁ ) / √s₁² / n₁ + s₂² / n₂

s₁ = 27 ⇒ s₁² = 729

n₁ = 45 ⇒ s₁² / n₁ = 16,2

s₂ = 7,56 ⇒ s₂² = 57,15

n₂ = 36 ⇒ s₂² / n₂ = 1,5876

√s₁² / n₁ + s₂² / n₂ = √ 16,2 + 1.5876 = 4,2175

z(s) = (23 - 25 )/4,2175

z(s) = - 0,4742

Comparing z(s) and z(c)

|z(s)| < | z(c)|

z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine

The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean

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Answers

The correct answer to this question is letter "B. We can't determine from the given information."

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Answers

Step-by-step explanation:

$(2)/(3) * (99)/(1) = 66 \: kg$

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Answers

The answer is the second one

Both the galapagos Islands and the island of naura are on the equator, but the galapagos Islands are at 90.30 degree West whereas the island of naura is at 166.56 degree east. How far is it from galapagos Islands to naura travelling over the pacific ocean along the equator, correct to the nearest km

Answers

Answer:

11481.4875 km

Step-by-step explanation:

Given the that :

Galapagos island and Island of Naura are on the equator

Galapagos = 90.30°W

Island of Naura = 166.56°E

Ensuring same bearing is used for both :

Island of Naura = 166.56°E = (360° - 166.56°) = 193.44°W

Hence, we can calculate the difference in the bearing of both locations :

(193.44 - 90.30)°W = 103.14°

Hence the distance between Galapagos and Island of Naura along the equator is :

(Difference in bearing / total bearing) * earth's Circumference

Earth's Circumference = 40,075km

(103.14 / 360) × 40,075

0.2865 × 40,075

= 11481.4875 km

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Answers

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A researcher records the repair cost for 8 randomly selected refrigerators. A sample mean of $57.89 and standard deviation of $23.69 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

The question is incomplete! the complete question along with answer and step by step explanation is provided below.

Question:

Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 2 : Construct the 95% confidence interval. Round your answer to two decimal places.

Given Information:

Sample mean repair cost = $57.89

Sample standard deviation = σ = $23.69

Sample size = 8

Confidence level = 95%

Required Information:

step 1: critical value = ?

step 2: 95% confidence interval = ?

Answer:

step 1: critical value = 2.365

step 2: 95% confidence interval = ($38.08, $77.70)

Step-by-step explanation:

Since the sample size is less than 30 and the standard deviation of the population is also unknown therefore, we can use the t-distribution to find the required confidence interval.

The confidence interval is given by

$CI = \bar{x} \pm MoE\n\n$

Where $\bar{x}$ is the mean repair cost and MoE is the margin of error that is given by

$$ MoE = t_(\alpha/2)((s)/(√(n) ) ) $ \n\n$

Where n is the sample size, s is the sample standard deviation, and $t_(\alpha/2)$ is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom (DoF) = n - 1 = 8 - 1 = 7

From the t-table at α = 0.025 and DoF = 7

t-score = 2.365

Therefore, the critical value that should be used in constructing the confidence interval is 2.365

$MoE = 2.365\cdot (23.69)/(√(8) ) \n\nMoE = 2.365\cdot 8.3756\n\nMoE = 19.808 \n\n$

So the required 95% confidence interval is

$CI = \bar{x} \pm MoE\n\nCI = 57.89 \pm 19.808\n\nCI = 57.89 - 19.808 \: and \: 57.89 + 19.808\n\nCI = \$38.08 \: and \:\:\$77.70\n$

Therefore, we are 95% confident that the mean repair cost for the refrigerators is within the range of ($38.08, $77.70)

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