Percent decrease from 64 to 21 round to the nearest percent<br><br> Thx :))

We are studying the proportion of cities that have private garbage collector. We want a maximum error of 0.10 and a 95% confiden

True [87]

Answer:

The minimum number of cities we need to contact is 96.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence interval

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

In this problem, we have that:

$p = 0.5, M = 0.1$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.1 = 1.96*\sqrt{\frac{0.5*0.5}{n}}$

$0.1\sqrt{n} = 0.98$

$\sqrt{n} = 9.8$

$(\sqrt{n})^{2} = (9.8)^{2}$

$n = 96$

The minimum number of cities we need to contact is 96.

8 0

2 years ago

Find the explicit formula for the given sequence.

Art [367]

Answer:

Option a.) an = -4(-3)^(n-1)

4 0

2 years ago

Please help thank you.

marusya05 [52]

This problem can be completed in 2 ways. Both are acceptable.

Option 1:

This is an isosceles trapezoid that can be divided into a rectangle and two congruent triangles.

The area of the rectangle is the base times the height.

$9 \times 4=36$

The area of one of the triangles is half the base times the height.

$\dfrac{1}{2} \times 5 \times 4 = 10$

The other triangle must have that area too.

$36+10+10=56$

The area is 56 square centimeters.

Option 2:

We can use the area formula for the trapezoid.

$A=\dfrac{b_1+b_2}{2} \times h$

Where $b_1$ is the length of the shorter base
and $b_2$ is the length of the longer base
and $h$ is the height.

The length of the shorter base is 9.
The length of the longer base is 9+5+5, or 19.

The height is 4.

$A=\dfrac{9+19}{2} \times 4$

$=56$

Same answer. The area is 56 square centimeters.

Both options are two acceptable ways the problem can be tackled.

7 0

3 years ago

Suppose the standard deviation of a normal population is known to be 3, and H0 asserts that the mean is equal to 12. A random sa

blagie [28]

Answer:

$z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9$

$p_v =P(z>1.9)=0.0287$

If we compare the p value and the significance level given $\alpha=0.05$ 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 true mean is higher than 12 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=12.95$ represent the sample mean

$\sigma=3$ represent the population standard deviation for the sample

$n=36$ sample size

$\mu_o =12$ represent the value that we want to test

$\alpha=0.05$ 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)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 12, the system of hypothesis would be:

Null hypothesis: $\mu \leq 12$

Alternative hypothesis: $\mu > 12$

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".

Calculate the statistic

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

$z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9$

P-value

Since is a right tailed test the p value would be:

$p_v =P(z>1.9)=0.0287$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ 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 true mean is higher than 12 at 5% of signficance.

4 0

3 years ago

Read 2 more answers

A candy box measures 8.2 cm in diameter and 15 cm in height. How many 2 cm cubed pieces of candy can fit into the box?

Katarina [22]

60 2cm candy prices can fit because if you multiply 8.2 by 15 it equals a decimal and if you divide it by 2 that the nearest whole number you’ll get is 60, so the answer has to be 60.

8 0

2 years ago

Percent decrease from 64 to 21 round to the nearest percent Thx :))