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3 years ago

15

The population of a school is 800 students and is increasing at a rate of 2% per year. Use an exponential function to find the p

opulation of the school after 9 years.

1 answer:

Mazyrski [523]3 years ago

5 0

Answer:

144 students in 9 years

Step-by-step explanation:

2%=0.02. 800×0.02=16

16×9=144

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In a recent year, a poll asked 2362 random adult citizens of a large country how they rated economic conditions. In the poll,

Harman [31]

Answer:

a) The 99% confidence interval is given by (0.198;0.242).

b) Based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

c) $\alpha=0.01$

Step-by-step explanation:

<em>Data given and notation </em>

n=2362 represent the random sample taken

X represent the people who says that they would watch one of the television shows.

$\hat p=\frac{X}{n}=0.22$ estimated proportion of people rated as Excellent/Good economic conditions.

$p_o=0.24$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest) <em> </em>

<em>Concepts and formulas to use </em>

We need to conduct a hypothesis in order to test the claim that 24% of people are rated with good economic conditions:

Null hypothesis: $p=0.24$

Alternative hypothesis: $p \neq 0.24$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Part a: Test the hypothesis

<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np = 2362x0.22=519.64>10 and n(1-p)=2364*(1-0.22)=1843.92>10

Condition satisfied.

<em>Calculate the statistic</em>

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.22 -0.24}{\sqrt{\frac{0.24(1-0.24)}{2362}}}=-2.28$

The confidence interval would be given by:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The critical value using $\alpha=0.01$ and $\alpha/2 =0.005$ would be $z_{\alpha/2}=2.58$ . Replacing the values given we have:

$0.22 - (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.198$

$0.22 + (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.242$

So the 99% confidence interval is given by (0.198;0.242).

Part b

<em>Statistical decision </em>

P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided is $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

So based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

Part c

The confidence level assumed was 99%, so then the signficance is given by $\alpha=1-confidence=1-0.99=0.01$

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3 years ago

Which two values are solutions to the inequality r ≤ 5?

sergij07 [2.7K]

Answer:

Step-by-step explanation:The solution is x > 3

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4 years ago

What is the recursive formula for the geometric sequence with this explicit formula?

IRINA_888 [86]

For the given geometric sequence, we have:

$a_1 = 9\\\\a_n = (-1/3)*a_{n-1}$

So the correct option is B.

<h3>Which is the recursive formula?</h3>

Here we have the geometric sequence:

$a_n = 9*(-\frac{1}{3} )^{(n - 1)}$

To get the initial value of the geometric sequence, we just need to replace n by 1, so we get:

$a_1 = 9*(-\frac{1}{3} )*(1 - 1) = 9$

Now, notice that the common ratio is (-1/3), this means that each term of the sequence is (-1/3) times the previous term.

$a_n = (-1/3)*a_{n-1}$

Then the correct option is B.

If you want to learn more about geometric sequences:

brainly.com/question/1509142

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2 years ago

Order from least to greatest 4.3, 3.4, 4.5, 3.45

kozerog [31]

Answer:

3.4, 3.45, 4.3, 4.5

Step-by-step explanation:

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3 years ago

Which steps will verify that a parrallelogram is a rectangle

Xelga [282]

Step-by-step explanation:

"To verify that a given parallelogram is a rectangle, you can calculate the lengths of all sides, and show that both pairs of opposite sides are congruent and calculate the slopes of every side, and show that adjacent sides are perpendicular."

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4 years ago