Mathematics, 13.11.2019 03:31 electrofy456

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered.

downtown store north mall store
sample size 25 20
sample mean $9 $8
sample standard deviation $2 $1
a 95% interval estimate for the difference between the two population means is

1.09 to 4.08

0.07 to 1.9

1.08 to 2.92

1.9 to 2.08

Answers: 2

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Answer from: reeseebaby89

0.07 to 1.9

Step-by-step explanation:

Let $\mu_1$ and $\mu_2$ be the population mean of hourly wages of employees of two branches of a department store (Downtown Store and North Mall Store)

As per given , we have

$n_1=25\\\\ n_2=20$

$\overline{x}_1=\$9\\\\\overline{x}_2=\$8$

$s_1=\$2\\\\s_1=\$1$

Degree of freedom : $\dfrac{(\dfrac{s_1^2}{n_1}+\dfrac{s _2^2}{n_2})^2}{\dfrac{(\dfrac{s_1^2}{n_1})^2}{n_1-1}+\dfrac{(\dfrac{s_2^2}{n_2})^2}{n_2-1}}$

$=\dfrac{(\dfrac{2^2}{25}+\dfrac{1^2}{20})^2}{\dfrac{(\dfrac{2^2}{25})^2}{24}+\dfrac{(\dfrac{1^2}{20})^2}{19}} =36$

Critical value for 95% confidence interval :

$t_{\alpha/2, df}=t_{0.025,\ 36}=2.028$

Then, 95% interval estimate for the difference between the two population means will be

$\overline{x}_1-\overline{x}_2\pm z_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s _2^2}{n_2}}$

$9-8\pm (2.028)\sqrt{\dfrac{2^2}{25}+\dfrac{1^2}{20}}$

$1\pm 0.93=(1-0.93,\ 1+0.93 ) = (0.07,\ 1.93)$

Hence, A 95% interval estimate for the difference between the two population means is (0.07, 1.93) .

i.e. 0.07 to 1.9

Answer from: Quest

Your pictures are upside down

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

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