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2 years ago

Growing up, Joe lived in a small town. When he left for college, the population was 840.

Mathematics

2 answers:

Ahat [919]2 years ago

5 0

Thé new population is 882

maria [59]2 years ago

3 0

Answer:

the population is 840 initially to which we subtract the 95% that leaves us a total of 42 to which we add the initial amount of population, which would give us as a final result 882

reply:

The total number of people that increased the population was 42 since Joe left, but in total there are 882 people.

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Answer:

There is enough evidence to claim that population mean 1 is less than population 2 at the 0.05 significance level.

Step-by-step explanation:

We are given the following in the question:

Group 1:

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Group 2:

$\mu_2 = 70.2\\\sigma_2 = 6.6\\n_2 = 13$

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

$H_{0}: \mu_1 \geq \mu_2\\H_A: \mu_1 < \mu_2$

Since, the population variances are equal and that the two populations are normally distributed, we use t-test(pooled test) for difference of two means.

Formula:

Pooled standard deviation

$s_p = \sqrt{\displaystyle\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2 }{n_1 + n_2 - 2}}$

$t_{stat} = \displaystyle\frac{\mu_1-\mu_2}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

$\text{Degree of freedom} = n_1 + n_2 - 2$

Putting all the values we get:

$s_p = \sqrt{\displaystyle\frac{(11-1)(3.7)^2 + (13-1)(6.6)^2 }{11 + 13 - 2}} = \sqrt{29.9827} = 5.48$

$t_{stat} = \displaystyle\frac{63.3-70.2}{5.48\sqrt{\frac{1}{11}+\frac{1}{13}}} = -3.073$

$\text{Degree of freedom} = 11 + 13 - 2 = 22$

Now,

$t_{critical} \text{ at 0.05 level of significance, 22 degree of freedom } = -1.717$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and reject the null hypothesis. We accept the alternate hypothesis.

We conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2.

There is enough evidence to claim that population mean 1 is less than population 2 at the 0.05 significance level.

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2 years ago

The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at ea

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Answer:

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Step-by-step explanation:

Given that,

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