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USPshnik [31]
2 years ago
7

With a capacity of 6,300 people, Royal Caribbean’s Oasis of the Seas is the world’s largest cruise ship. The average beer consum

ption over 35 randomly selected seven-day cruises on the ship was 81,740 bottles. From historical data you know that the population standard deviation of beer consumption is 4,590 bottles. Royal Caribbean would like to estimate the average beer consumption to plan its beer inventory levels on future cruises. (The ship certainly doesn’t want to run out of beer in the middle of the ocean!)
A. Construct a 95% confidence interval to estimate the average beer consumption per cruise.
B. Verify this interval using excel.
C. What assumptions need to be made about this population?
Mathematics
1 answer:
Mariulka [41]2 years ago
6 0

Step-by-step explanation:

Mean = 81740

Standard deviation = 4590

Sample size = 15

Alpha level = 1-0.95 = 0.05

Df = 15-1 = 14

Critical value:

alpha/2 = 0.05/2 = 0.05

t0.025

t critical value = 2.145

Margin of error ME

2.145 x 4590/√15

2.145 x 4590/3.873

ME = 2542.09

Confidence interval

Lower CI = mean - ME

= 81740-2542.09

= 79197.91

Upper CI = mean + ME

= 81740+2542.09

= 84282.09

[ 79197.91, 84282.09]

B.

Using excel, exact answer for CI

Lower limit = 79198.142724212173

Upper limit = 84281.8572757827

C.

The assumptions to be made from the population are that

1. Samples are random

2. These samples are gotten from an approximately normal distribution

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Please solve (a^3 - 2a^2) - (3a^2 - 4a^3).
Wittaler [7]

Hi there! Hopefully this helps!

-------------------------------------------------------------------------------------------------------

<h2>Answer: 5a^{3} - 5a^{2}. </h2><h2 /><h2>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</h2><h2 />

|(a^{3} - 2a^{2}) - (3a^{2} - 4a^{3} )

|

| To find the opposite of 3a^{2} -4a^{3}, find the <em>opposite</em> of each term.

\/

a^{3} - 2a^{2} - 3a^{2} + 4a^{3}

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

|

|Combine -2a^{2} and -3a^{2} to get -5a^{2}.

\/

a^{3} - 5a^{2} + 4a^{3}

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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|Combine a^{3} and 4a^{3} to get 5a^{3}.

\/

<h2>Answer: 5a^{3} - 5a^{2}</h2>
8 0
3 years ago
At a local department store, cardigans are typically priced at $15. Due to a special,
nevsk [136]

Answer:

$3

Step-by-step explanation:

80% of 15 is 12

15-12=3

4 0
3 years ago
PLEASE HELP! Which number is a rational number?
8090 [49]

Answer:

C. 17.156

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal. It can be expressed as a ratio of two integers.

The first answer wouldn't make sense, because there is no number times itself that would equal 15. Therefore, it would be irrational. Same goes with the last option.

We can also automatically rule out the second option because it is a nonterminating decimal.

8 0
3 years ago
What is the slope of the line that passes through the pair of points? (1, 7), (10, 1)
Valentin [98]
The slope of the line can be calculated as:

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8 0
3 years ago
Read 2 more answers
The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed.
tatuchka [14]

Answer:

a)Null hypothesis:- H₀: μ> 500

  Alternative hypothesis:-H₁ : μ< 500

b) (5211.05 , 5411.7)

95% lower confidence bound on the mean.

c) The test of hypothesis t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Step-by-step explanation:

<u>Step :-1</u>

Given  a random sample of 15 devices is selected in the laboratory.

size of the small sample 'n' = 15

An average life of 5311.4 hours and a sample standard deviation of 220.7 hours.

Average of sample mean (x⁻) =  5311.4 hours

sample standard deviation (S) = 220.7 hours.

<u>Step :- 2</u>

<u>a) Null hypothesis</u>:- H₀: μ> 500

<u>Alternative hypothesis</u>:-H₁ : μ< 500

<u>Level of significance</u> :- α = 0.95 or 0.05

b) The test statistic

t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n-1} } }

t = \frac{5311.4 - 500}{\frac{220.7}{\sqrt{15-1} } }

t = 5.826

The degrees of freedom γ= n-1 = 15-1 =14

tabulated value t =1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

calculated value t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Null hypothesis is rejected at  95% confidence on the mean.

C) <u>The 95% of confidence limits </u>

(x^{-} - t_{0.05} \frac{S}{\sqrt{n} } ,x^{-} + t_{0.05}\frac{S}{\sqrt{n} } )

substitute values and simplification , we get

(5311.4 - 1.761 \frac{220.7}{\sqrt{15} } ,5311.4 +1.761\frac{220.7}{\sqrt{15} } )

(5211.05 , 5411.7)

95% lower confidence bound on the mean.

5 0
3 years ago
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