What's the algebraic expression for n cubed increased by 5??

Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below.

garik1379 [7]

Answer:

The 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

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".

$\bar X_1 =9.2$ represent the sample mean 1

$\bar X_2 =8.8$ represent the sample mean 2

n1=27 represent the sample 1 size

n2=30 represent the sample 2 size

$\sigma_1 =0.3$ population standard deviation for sample 1

$\sigma_2 =0.1$ population standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Solution to the problem

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =9.2-8.8=0.4$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$0.4-1.96\sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}=0.281$

$0.4+1.96\sqrt{\frac{6^2}{36}+\frac{7^}{49}}=0.519$

So on this case the 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

6 0

3 years ago

The ratio of working-age population to the elderly in the United States (including projections after 2000) is given by the funct

Dovator [93]

Answer:

a) Sketch the graph of the function f. (it is in the attached file)

b) What was the ratio at the beginning of 2006? At the beginning of 2014?

For 2006 the ratio is 3.92

For 2014 the ratio is 3.5

c) Over what years is the ratio constant?

[1995, 2000]

d) Over what years is the decline of the ratio greatest?

[2010, 2030]

Step-by-step explanation:

b) We first need to know in between which function 2006 falls into, so if we start in t=0=1995, then 2006-1995=11, t=11

t=11 fall into:

$f(x)=-0.03t+4.25$

$f(11)=-0.03(11)+4.25=3.92$

For 2006 the ratio is 3.92

2014:

Same process that 2006, t=0=1995, then 2014-1995=19, t=19

t=19fall into:

$f(x)=-0.075t+4.925$

$f(19)=-0.075(11)+4.925=3.5$

For 2014 the ratio is 3.5

c) The ratio is only constant in the first section of the graph 0≤t<5, since 4.1 is constant. Following the same process for the years in star (b) we have t=0, 1995+0=1995, t=5, 1995+5=2000.

The ratio will be constant between [1995, 2000]

d) For the greatest decline we need to compare slopes. From the line equation we have:

$y(x)=mx+b$ where m is the slope and b is the point the line intersects with the y axis. Here we have: