Find a. Write your answer in simplest radical form.

A average amount of money on deposit in a savings account is $7500. Suppose a random sample of 49 accounts shows the average in

Valentin [98]

Answer:

z=-3.79

$p_v =2*P(z$

Step-by-step explanation:

1) Data given and notation

$\bar X=6850$ represent the mean average amount of money on deposit in savings account for the sample

$\sigma=1200$ represent the population standard deviation for the sample

$n=49$ sample size

$\mu_o =7500$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the amount of money on deposit in savings account differs from 7500, the system of hypothesis would be:

Null hypothesis: $\mu =7500$

Alternative hypothesis: $\mu \neq 7500$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{6850-7500}{\frac{1200}{\sqrt{49}}}=-3.79$

4)P-value

Since is a two-sided test the p value would be:

$p_v =2*P(z$

5) Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the average amount of money deposit in savings account its significantly different from 7500 tons at 1% of signficance.

7 0

3 years ago

Ntate runs 12 km in 3 hours. how many hours will it take him to run in 1 km

docker41 [41]

Answer:

15 minutes or 1/4 hour

Step-by-step explanation:

3 hours = 60*3=180

180/12=15

5 0

2 years ago

180° < x < 270°, what is the value of tan-1(0.577)?

Allisa [31]

Think: "Find <span>tan-1(0.577)" means "Find the ANGLE in Quadrant III whose tangent is 0.577. Because the angle is in QIII, both the opp side and the adj side are negative. Here you have four answer choices. The correct answer MUST be within the interval 180 and 270 degrees. Only one of the given answer choices satisfies that criterion. Which one is it?

</span><span>tan-1(0.577) = ?</span>

7 0

3 years ago

A poll conducted in 2013 found that 55% of U.S. adult Twitter users get at least some news on Twitter (Pew, 2013). The standard

alina1380 [7]

Answer:

The 99% confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter is between 49.34% and 60.66%, which means that we are 99% sure that the true percentage of US adult Twitter users who get some news is in this interval.

Step-by-step explanation:

Confidence interval:

A confidence interval has the following format:

$M \pm zs$

In which M is the sample mean, z is related to the confidence level and s is the standard error.

55% of U.S. adult Twitter users get at least some news on Twitter (Pew, 2013). The standard error for this estimate was 2.2%.

This means that $M = 55, s = 2.2$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

Lower bound of the interval:

$M - zs = 55 - 2.575*2.2 = 49.34$

Upper bound:

$M + zs = 55 + 2.575*2.2 = 60.66$

The 99% confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter is between 49.34% and 60.66%, which means that we are 99% sure that the true percentage of US adult Twitter users who get some news is in this interval.

6 0

3 years ago

A suitcase measures 24 inches long and -8 i aches high. What is the diagonal length of the suitcase? (Pythagorean Theorem)

BartSMP [9]

Answer:

Diagonal Length = $8\sqrt{10}$ inches

Step-by-step explanation:

The suitcase is a rectangle with one side being 24 and another side being 8.

The diagonal is the line through the middle connecting two opposite corners.

If we draw the diagonal, it creates a triangle with one leg being 24 and another being 8.

The diagonal is the "hypotenuse" of the triangle.

Now, the pythagorean theorem:

leg^2 + another leg^2 = hypotenuse^2

So, we substitute the values known and find the hypotenuse (which is length of the diagonal). Shown below:

$24^2+8^2=h^2\\640=h^2\\h=\sqrt{640}\\h=\sqrt{64*10}\\h=\sqrt{64}\sqrt{10}\\h=8\sqrt{10}$

We have written the answer in exact form (with radical in simplified term).

We also use the radical property $\sqrt{a*b}=\sqrt{a}\sqrt{b}$

7 0

3 years ago