15) 5,25 , 125 ,625 ,3125<br>Rule =

Two machines are used for filling glass bottles with a soft-drink beverage. The filling process have known standard deviations s

stellarik [79]

Answer:

a. We reject the null hypothesis at the significance level of 0.05

b. The p-value is zero for practical applications

c. (-0.0225, -0.0375)

Step-by-step explanation:

Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.

Then we have $n_{1} = 25$ , $\bar{x}_{1} = 2.04$ , $\sigma_{1} = 0.010$ and $n_{2} = 20$ , $\bar{x}_{2} = 2.07$ , $\sigma_{2} = 0.015$ . The pooled estimate is given by

$\sigma_{p}^{2} = \frac{(n_{1}-1)\sigma_{1}^{2}+(n_{2}-1)\sigma_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(25-1)(0.010)^{2}+(20-1)(0.015)^{2}}{25+20-2} = 0.0001552$

a. We want to test $H_{0}: \mu_{1}-\mu_{2} = 0$ vs $H_{1}: \mu_{1}-\mu_{2} \neq 0$ (two-tailed alternative).

The test statistic is $T = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{S_{p}\sqrt{1/n_{1}+1/n_{2}}}$ and the observed value is $t_{0} = \frac{2.04 - 2.07}{(0.01246)(0.3)} = -8.0257$ . T has a Student's t distribution with 20 + 25 - 2 = 43 df.

The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value $t_{0}$ falls inside RR, we reject the null hypothesis at the significance level of 0.05

b. The p-value for this test is given by $2P(T$ 0 (4.359564e-10) because we have a two-tailed alternative. Here T has a t distribution with 43 df.

c. The 95% confidence interval for the true mean difference is given by (if the samples are independent)

$(\bar{x}_{1}-\bar{x}_{2})\pm t_{0.05/2}s_{p}\sqrt{\frac{1}{25}+\frac{1}{20}}$ , i.e.,

$-0.03\pm t_{0.025}0.012459\sqrt{\frac{1}{25}+\frac{1}{20}}$

where $t_{0.025}$ is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So

$-0.03\pm(2.0167)(0.012459)(0.3)$ , i.e.,

(-0.0225, -0.0375)

8 0

2 years ago

Suppose the current cost of gasoline is

Elodia [21]

Answer:

The current price index number is $604.2.

Step-by-step explanation:

The index value is the ratio between the current value and the reference value, multiplied by 100.

In this problem, we have that:

Current value = $3.48

Reference value: $0.576

Index price = (3.48/0.576)*100 = $604.2.

The current price index number is $604.2.

4 0

3 years ago

Please hurry and answer<br> i need this asap

Afina-wow [57]

It represent 13,9
Hope this helps

6 0

2 years ago

Stern MASS ASB is doing a Valentine’s Day Fundraiser. They are selling roses for $3 each and carnations for $2 each.They sold a

horrorfan [7]

Answer:

They sold

20 Roses and 20 Carnations

Step-by-step explanation:

The total sales of 40 flowers is $100 not $10 as in the question

Roses=$3

Carnations=$2

Total flowers sold=40

Total sales=$10

Let Roses=r

Carnations=c

c+r=40. (1)

3r+2c=100 (2)

From (1)

c=40-r

Substitute c=40-r into (2)

3r+2c=100

3r+2(40-r)=100

3r+80-2r=10

r=100-80

r=20

Substitute r=20 into (1)

c+r=40

c+20=40

c=40-20

=20

c=20

r=20

Check:

3r+2c=100

3(20)+2(20)=100

60+40=100

100=100

4 0

2 years ago

Order of Operations With Integers. Please help me solve and how you got the answer!! help, please!!

Nuetrik [128]

Answer:

2

Step-by-step explanation:

$\frac{(-2)(-3)(-4)}{-9 + (-3)}$

First, simplify the top and bottom separately:

$\frac{-24}{-12}$

Then, just divide:

$-24 / -12 = 2$

7 0

2 years ago

15) 5,25 , 125 ,625 ,3125Rule =​

15) 5,25 , 125 ,625 ,3125Rule =