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hichkok12 [17]
3 years ago
12

4. Find the percent of increase from 56 to 70. Round your answer

Mathematics
1 answer:
notsponge [240]3 years ago
6 0

Answer:

25%

Step-by-step explanation:

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In a simple random sample of 14001400 young​ people, 9090​% had earned a high school diploma. Complete parts a through d below.
ratelena [41]

Answer:

(a) The standard error is 0.0080.

(b) The margin of error is 1.6%.

(c) The 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

(d) The percentage of young people who earn high school diplomas has ​increased.

Step-by-step explanation:

Let <em>p</em> = proportion of young people who had earned a high school diploma.

A sample of <em>n</em> = 1400 young people are selected.

The sample proportion of young people who had earned a high school diploma is:

\hat p=0.90

(a)

The standard error for the estimate of the percentage of all young people who earned a high school​ diploma is given by:

SE_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}

Compute the standard error value as follows:

SE_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}

       =\sqrt{\frac{0.90(1-0.90)}{1400}}\\

       =0.008

Thus, the standard error for the estimate of the percentage of all young people who earned a high school​ diploma is 0.0080.

(b)

The margin of error for (1 - <em>α</em>)% confidence interval for population proportion is:

MOE=z_{\alpha/2}\times SE_{\hat p}

Compute the critical value of <em>z</em> for 95% confidence level as follows:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Compute the margin of error as follows:

MOE=z_{\alpha/2}\times SE_{\hat p}

          =1.96\times 0.0080\\=0.01568\\\approx1.6\%

Thus, the margin of error is 1.6%.

(c)

Compute the 95% confidence interval for population proportion as follows:

CI=\hat p\pm MOE\\=0.90\pm 0.016\\=(0.884, 0.916)\\\approx (88.4\%,\ 91.6\%)

Thus, the 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

(d)

To test whether the percentage of young people who earn high school diplomas has​ increased, the hypothesis is defined as:

<em>H₀</em>: The percentage of young people who earn high school diplomas has not​ increased, i.e. <em>p</em> = 0.80.

<em>Hₐ</em>: The percentage of young people who earn high school diplomas has not​ increased, i.e. <em>p</em> > 0.80.

Decision rule:

If the 95% confidence interval for proportions consists the null value, i.e. 0.80, then the null hypothesis will not be rejected and vice-versa.

The 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

The confidence interval does not consist the null value of <em>p</em>, i.e. 0.80.

Thus, the null hypothesis is rejected.

Hence, it can be concluded that the percentage of young people who earn high school diplomas has ​increased.

8 0
3 years ago
A car is moving at a speed of 50 km/hour. The driver takes her foot off of the accelerator and the car coasts to a stop. Why? A)
velikii [3]

C) without an external energy source, fiction stops the car

<em>Sure hope this helps you</em>

4 0
2 years ago
Read 2 more answers
Peter is the owner of a hotel. He has found that when he charges the nightly cost of $139, the average occupancy is 275. In addi
zimovet [89]

Answer:

Without price increase, Cost/night = $119

Average occupancy = 372 The revenue will be 119*372 = $44,268

For every $15 price increase, the occupancy decreases by 25. Therefore with x price increases, The revenue will be $(119 + 15x)*(372 25x)

Cost/night = $119 + 15x Occupancy = 372 - 25x

Answer:

The nightly cost with x $15 price increases is $119 + 15x.

3 0
2 years ago
This equation shows how the accuracy of Alexa's watch is related to how long it's been since she last set it.
Kruka [31]

Answer:

2

Step-by-step explanantion:

You sustitute 20 for s to get 20 = d + 18, subtract 18 from both sides and you get d = 2.

4 0
3 years ago
Please help me 7.2 × 2.1
Varvara68 [4.7K]

Answer:

15.12

Step-by-step explanation:

That's the a water to ur question.

hope it helps.

Have a good day and stay safe!

5 0
3 years ago
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