Mathematics, 08.07.2020 19:01 mia1518

You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 63. While it is an uncommon confidence interval, find the critical valuebthat corresponds tona confidence interval of 81.2%.

Answers: 3

Show answers

Answers

Answer from: ariannayazmin052509

The critical value that corresponds to a confidence interval of 81.2% is 1.32.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the sample means is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the sample means is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

In this case the sample selected is of size, n = 63.

As the sample size n = 63 > 30, the sampling distribution of sample mean will be approximately normal.

So, a z-interval will be used to estimate the population mean.

The confidence level is, 81.2%.

The value of α is:

$\alpha=1-\text{Confidence Level}\\\\\alpha=1-0.812\\\\\alpha=0.188$

The critical value is:

$z_{\alpha/2}=z_{0.188/2}=z_{0.094}=- 1.32\\\\z_{1-\alpha/2}=z_{1-0.188/2}=z_{0.906}= 1.32$

*Use a z-table.

Thus, the critical value that corresponds to a confidence interval of 81.2% is 1.32.

Answer from: Quest

Ithink it is correct but just ask someone else but i am sure it it

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Another question on Mathematics

Mathematics, 21.06.2019 15:50

Create and solve a linear equation that represents the model, where squares and triangles are shown evenly balanced on a balance beam. assume the weight of a square is 1 unit and the weight of a triangle is unknown.

Answers: 3

Answer

Mathematics, 21.06.2019 19:00

Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. x^2 - 23 = 10x a. -1.93, 11.93 b. 1.93, -11.93 c. 1.93, 11.93 d. -1.93, -11.93

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

Find cot x if sin x cot x csc x = √2

Answers: 2

Answer

Mathematics, 21.06.2019 22:20

Which strategy is used by public health to reduce the incidence of food poisoning?

Answers: 1

Answer

You know the right answer?

You intend to estimate a population mean with a confidence interval. You believe the population to h...