Is there a such thing as a zillion?

Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below. Find the 93% conf

kobusy [5.1K]

Answer:

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

And replacing we got:

$(9.2 -8.8) - 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.2903$

$(9.2 -8.8) + 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.5097$

And the confidence interval for the difference of means would be given by:

$0.2903 \leq \mu_1 -\mu_2 \leq 0.5097$

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".

We have the following data given:

$\bar X_1 = 9.2 , \bar X_2 = 8.8, \sigma_1= 0.3, n_1 = 27, \sigma_2 = 0.1, n_2 = 30$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 93% of confidence, our significance level would be given by $\alpha=1-0.93=0.07$ and $\alpha/2 =0.035$ . And the critical value would be given by:

$z_{\alpha/2}=-1.811, z_{1-\alpha/2}=1.811$

The confidence interval is given by:

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

And replacing we got:

$(9.2 -8.8) - 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.2903$

$(9.2 -8.8) + 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.5097$

And the confidence interval for the difference of means would be given by:

$0.2903 \leq \mu_1 -\mu_2 \leq 0.5097$

4 0

3 years ago

PLEASE HELP I NEED THIS DONE Chan deposited money into his retirement account that is compounded annually at an interest rate of

rjkz [21]

Answer:

No, equivalent quarterly rate will be approx 1.75%

Step-by-step explanation:

Given that Chan deposited money into his retirement account that is compounded annually at an interest rate of 7%.

We know that there are 4 quarters in 1 year.

So to find that equivalent quarterly we will divide given yearly rate by number of quarters.

That means divide 7% by 4.

which gives 1.75%.

But that is different than Chan's though of 2% quarterly interest.

Hence Chan is wrong.

8 0

3 years ago

..................................

Annette [7]

Answer:

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Step-by-step explanation:

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6 0

3 years ago

The population of the united states is 280 million. If 2 out of 3 americans know who the vice president is, how many americans k

kotykmax [81]

Answer:

186,666,667 Americans know who the vice president is

Step-by-step explanation:

In this question, we are tasked with calculating the number of USA citizens that know who the vice president is.

Now, in this question, we are made to know that the total population is set at 280 million with 2 out of three knowing who the vice president is.

What this means is that a fraction of the population at 2/3 knows who the vice president is

This fraction is equal to; 2/3 * 280,000,000 = 186,666,666.66666666

This is approximately equal to 186,666,667 people

8 0

3 years ago

Read 2 more answers

A={1,2,3} set-builder notation

Irina18 [472]

A = {x|x∈N,x<4} = {1,2,3}

6 0

3 years ago