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Sladkaya [172]
3 years ago
11

A battery manufacturer advertises that the mean reserve capacity of a certain battery is 1500 hours. You suspect that the batter

ies’ reserve time is less than the advertised value. To test this claim, you randomly select a sample of 20 batteries and find the mean reserve capacity to be 1320 hours. Assume that the population standard deviation is 320 hours. Do you have enough evidence to support the manufacturer’s claim? What assumption is necessary for this test to be valid? None. The Central Limit Theorem makes any assumptions unnecessary. The population of all the batteries’ reserve time is normally distributed because of the small sample size. The population variance must equal the population mean.
Mathematics
1 answer:
alexdok [17]3 years ago
8 0

Answer:

The test statistic t =  2.45 > 1.729

we rejected null hypothesis so the population mean is not equal population variance

Step-by-step explanation:

The mean reserve capacity of a certain battery is(μ) 1500 hours

Given sample of  n = 20 batteries

The sample mean reserve capacity to be (x)=1320 hours.

Assume that the population standard deviation is(σ) = 320 hours

Null hypothesis:H0 = μ = 1500 hours

Alternative hypothesis:H1 = μ ≠ 1500 hours

The test statistic

t = \frac{x-u}{\frac{σ}{\sqrt{n} } }

now simplification, we get

t = \frac{1320-1500}{\frac{320}{\sqrt{20-1} } }

t = modulus(-2.45) = 2.45

Degrees of freedom γ = n-1 = 20-1 =19

By tabulated value in t- distribution at 5% level of significance

tabulated value = 1.729 ( from table)

The calculated value > tabulated value

we rejected null hypothesis .

we rejected null hypothesis so the population mean is not equal population variance

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Mrrafil [7]

Answer:

The contestant should try and answer question 2 first to maximize the expected reward.

Step-by-step explanation:

Let the probability of getting question 1 right = P(A) = 0.60

Probability of not getting question 1 = P(A') = 1 - P(A) = 1 - 0.60 = 0.40

Let the probability of getting question 2 right be = P(B) = 0.80

Probability of not getting question 2 = P(B') = 1 - P(B) = 1 - 0.80 = 0.20

To obtain the better option using the expected value method.

E(X) = Σ xᵢpᵢ

where pᵢ = each probability.

xᵢ = cash reward for each probability.

There are two ways to go about this.

Approach 1

If the contestant attempts question 1 first.

The possible probabilities include

1) The contestant misses the question 1 and cannot answer question 2 = P(A') = 0.40; cash reward associated = $0

2) The contestant gets the question 1 and misses question 2 = P(A n B') = P(A) × P(B') = 0.6 × 0.2 = 0.12; cash reward associated with this probability = $200

3) The contestant gets the question 1 and gets the question 2 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300

Expected reward for this approach

E(X) = (0.4×0) + (0.12×200) + (0.48×300) = $168

Approach 2

If the contestant attempts question 2 first.

The possible probabilities include

1) The contestant misses the question 2 and cannot answer question 1 = P(B') = 0.20; cash reward associated = $0

2) The contestant gets the question 2 and misses question 1 = P(A' n B) = P(A') × P(B) = 0.4 × 0.8 = 0.32; cash reward associated with this probability = $100

3) The contestant gets the question 2 and gets the question 1 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300

Expected reward for this approach

E(X) = (0.2×0) + (0.32×100) + (0.48×300) = $176

Approach 2 is the better approach to follow as it has a higher expected reward.

The contestant should try and answer question 2 first to maximize the expected reward.

Hope this helps!!!

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96/6= 6y^2 / 6
16=y^2
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Answer:

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<em />

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