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Sladkaya [172]
3 years ago
10

Two​ trains, Train A and Train​ B, weigh a total of 300 tons. Train A is heavier than Train B. The difference of their weights i

s 128 tons. What is the weight of each​ train?
Mathematics
1 answer:
eduard3 years ago
7 0

Answer:

Train A = 214

Train B = 86

Step-by-step explanation:

a + b = 300

a - b = 128

a + b = 300

a = 128 + b

(128 + b) + b = 300

128 + b + b = 300

128 + 2b = 300

2b = 300 - 128

2b = 172

b = 172 ÷ 2

b = 86

a = 128 + b

a = 128 + (86)

a = 214

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We conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.

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We are given that a survey showed that among 785 randomly selected subjects who completed four years of college, 144 of them are smokers.

Let p = <u><em>population proportion of smokers among those with four years of college</em></u>

So, Null Hypothesis, H_0 : p \geq 27%      {means that the rate of smoking among those with four years of college is more than or equal to the 27% rate for the general population}

Alternate Hypothesis, H_A : p < 27%      {means that the rate of smoking among those with four years of college is less than the 27% rate for the general population}

The test statistics that will be used here is <u>One-sample z-test</u> for proportions;

                             T.S.  =  \frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }  ~   N(0,1)

where, \hat p = sample proportion of smokers = \frac{144}{785} = 0.18

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So, <em><u>the test statistics</u></em> =  \frac{0.18-0.27}{\sqrt{\frac{0.27(1-0.27)}{785} } }

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The value of z-test statistics is -5.68.

<h2>Also, the P-value of the test statistics is given by;</h2>

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Now, at a 0.01 level of significance, the z table gives a critical value of -2.3262 for the left-tailed test.

Since the value of our test statistics is less than the critical value of z, so we have <u><em>sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.

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