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3 years ago

14

A frequenter of a pub had observed that the new barman poured in average 0.47 liters of beer into the glass with a standard devi

ation equal to 0.09 liters instead of a half a liter with the same standard deviation. The frequenter had used a random sample of 47 glasses of beer in his experiment. Consider the one-sided hypothesis test for volume of beer in a glass: H0: u=0.5 against H1: u<0.5. Determine the P-value of this test.
Round your answer to four decimal places (e.g. 98.7654).

1 answer:

aalyn [17]3 years ago

6 0

Answer:

P-value = 0.0011

Explanation:

Formula for the test statistic is;

z = (x¯ - μ)/(σ/√n)

We have;

Sample mean;x¯ = 0.47

Population mean; μ = 0.5

Standard deviation; σ = 0.09

Sample size; n = 47

Thus;

z = (0.46 - 0.5)/(0.09/√47)

z = -3.05

From z-distribution table attached, the p-value corresponding to z = -3.05 is;

P = 0.00114

To four decimal places gives;

P-value = 0.0011

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2 years ago

1. An automobile travels along a straight road at 15.65 m/s through a 11.18 m/s

djyliett [7]

Answer:

a.) Time = 17.13 seconds

b.) 31.88 m

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d.) V = 7.1 m/s

Explanation:

The initial velocity U of the automobile is 15.65 m/s.

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t = 15.65/3.05

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But the motorist noticed the police car in his rear view mirror 12 s after the police car started the pursuit and applied his brakes and decelerates at 3.05 m/s².

The total time required for the police car to overtake the automobile will be

12 + 5.13 = 17.13 seconds.

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11.18^2 = 0 + 2 × 1.96 ×S

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S = 124.99/3.92

S = 31.88 m

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3 years ago

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2 years ago

700.0 liters of a gas are prepared at 760.0 mmHg and 100.0 °C. The gas is placed into a tank under high pressure. When the tank

ololo11 [35]

Answer:

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When the gas is in the thank we have:

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By entering equation (2) into (1) we have:

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I hope it helps you!

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3 years ago

A spark ignition engine burns a fuel of calorific value 45MJkg. It compresses the air-ful mixture in accordance with PV^1.3=cons

antoniya [11.8K]

Answer:

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ii). fuel consumption = 0.4947 kg/hr

Explanation:

Given :

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where $r_{c}$ is compression ratio = $\frac{v_{c}+v_{s}}{v_{c}}$

$r_{c}$ = $1+\frac{v_{s}}{v_{c}}$

where $v_{c}$ is compression volume

$v_{s}$ is swept volume

Now it is given that swept volume at 30% of compression, 70% of the swept volume remains.

Then, $v_{30}=v_{c}+0.7v_{s}$

and at 70% compression, 30% of the swept volume remains

∴ $v_{70}=v_{c}+0.3v_{s}$

We know,

$\frac{P_{2}}{P_{1}}=\left ( \frac{V_{1}}{V_{2}} \right )^{n}$

$\frac{2.75}{1.5}=\left ( \frac{v_{c}+0.7\times v_{s}}{v_{c}+0.3\times v_{s}} \right )^{1.3}$

$\left ( 1.833 \right )^{\frac{1}{1.3}}=\frac{v_{c}+0.7v_{s}}{v_{c}+0.3v_{s}}\\$

$1.594=\frac{v_{c}+0.7v_{s}}{v_{c}+0.3v_{s}}$

$v_{c}+0.7v_{s}=1.594v_{c}+0.4782v_{s}$

$0.7v_{s}-0.4782v_{s}=1.594v_{c}-v_{c}$

$0.2218v_{s} = 0.594v_{c}$

$v_{c}=0.3734 v_{s}$

∴ $r_{c}= 1+\frac{v_{s}}{0.3734v_{s}}$

Therefore, compression ratio is $r_{c}$ = 3.678

Now efficiency, $\eta =\left ( 1-\frac{1}{r_{c}} \right )^{0.3}$

$\eta =\left ( 1-\frac{1}{3.678} \right )^{0.3}$

$\eta =0.32342$ , this is the ideal efficiency

Therefore actual efficiency, $\eta_{act} =0.5\times \eta _{ideal}$

$\eta_{act} =0.5\times 0.32342$

$\eta_{act} =0.1617$

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= 3600 kJ

∴ we know efficiency, $\eta=\frac{W_{net}}{Q_{supply}}$

$Q_{supply}=\frac{W_{net}}{\eta _{act}}$

$Q_{supply}=\frac{3600}{0.1617}$

$Q_{supply}=22261.78 kJ$

Therefore fuel required = $\frac{22261.78}{45000}$

= 0.4947 kg/hr

5 0

3 years ago