Mathematics, 25.02.2020 23:52 jjelzy

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses. It wants 95 percent confidence and will select a sample of 10 men and 10 women for the study. The variances are assumed equal and the populations normally distributed. The sample results are:

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Answer from: sIatt

$s^2_p = \frac{9*0.3^2 +9*0.4^2}{10+10-2}=0.125$

$s_p =\sqrt{0.125}=0.354$

$(2.7 -2.4) - 2.1*0.354\sqrt{\frac{1}{10}+\frac{1}{10}}=-0.032$

$(2.7 -2.4)+ 2.1*0.354\sqrt{\frac{1}{10}+\frac{1}{10}}=0.632$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data given

$\bar X_M = 2.7$ represent the sample mean for men

$\bar X_F = 2.4$ represent the sample mean for women

s_M = 0.3 represent the sample deviation for men

s_F = 0.4 represent the sample deviation for women

n_M = 10 sample size of male

n_F =10 sample size of women

The confidence interval is given by:

$(\bar X_M -\bar X_F) \pm t_{\alpha/2} S_p \sqrt{\frac{1}{n_M}+\frac{1}{n_F}}$ (1)

The polled variance can be calculated with this formula:

$s^2_p = \frac{9*0.3^2 +9*0.4^2}{10+10-2}=0.125$

$s_p =\sqrt{0.125}=0.354$

For a confidence of 95% the value for the significance is $\alpha=1-0.95=0.05$ and $\alpha/2 = 0.025$ , the degrees of freedom are given by:

df = n_M + n_F -2= 10+10-2=18

And the critical value can be calculated with the following formula in excel: "=T.INV(1-0.025,18)" and we got $t_{\alpha/2}=2.1$

Now we can replace into the confidence interval:

$(2.7 -2.4) - 2.1*0.354\sqrt{\frac{1}{10}+\frac{1}{10}}=-0.032$

$(2.7 -2.4)+ 2.1*0.354\sqrt{\frac{1}{10}+\frac{1}{10}}=0.632$

Answer from: Quest

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes.

step-by-step explanation:

Answer from: Quest

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.

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