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2 years ago

The first tern of an arithmetic sequence is -3 and the fifteenth term id 53. What is the common difference of the sequence?

1 answer:

5 0

The common difference is 4. U know that the formula is the first term + d(n -1). N-1 is 14 so u know that 14 times a number needs to equal 56 because the first term is -3 and 56-3 is 53. 14 * 4 is 56. So the common difference is 4

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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 p = proportion of young people who had earned a high school diploma.

A sample of n = 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 - α)% confidence interval for population proportion is:

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

Compute the critical value of z 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:

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

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

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3 years ago

Juan has 24 marbles and 6 bags Write a number sentence that shows how many marbles he can put in each bag if he puts the same nu

I am Lyosha [343]

24 divided by 6=3 is the answer

7 0

2 years ago

Read 2 more answers

Which of the following verbal expression represents the algebraic expression x/2+5

ycow [4]

It would be 5 more than half of a number.

6 0

3 years ago

Answer this ASAP! URGENT

kobusy [5.1K]

Answer:

6th square -2

8th square -3

9th square -8

Step-by-step explanation: The sum is -12

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3 years ago

James invests some money into an account that pays 4% compounded annually. If the account has $851.66 after 5 years, how much di

Charra [1.4K]

Answer:

the third option, "what number, when added to negative four, is equal to negative five?"

Step-by-step explanation:

"what number, when added to negative four, is equal to negative five?" can be expressed as g + (- 4) = - 5, which is the same as in the equation.

i hope this helps! :D comment if you need any clarification.

6 0

2 years ago