If two numbers have the same sign, then their sum is always positive.

Confidence Interval Mistakes and Misunderstandingsâ€”Suppose that 500 randomly selected recent graduates of a university were as

kvv77 [185]

Answer:

The correct 95% confidence interval is (8.4, 8.8).

Step-by-step explanation:

The information provided is:

$n=500\\\bar x=8.6\\\sigma=2.2$

(a)

The (1 - α)% confidence interval for population mean (μ) is:

$CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}$

The 95% confidence interval for the average satisfaction score is computed as:

8.6 ± 1.96 (2.2)

This confidence interval is incorrect.

Because the critical value is multiplied directly by the standard deviation.

The correct interval is:

$8.6\pm 1.96 (\frac{2.2}{\sqrt{500}})=8.6\pm 0.20=(8.4,\ 8.6)$

(b)

The (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence interval for the mean rating, (8.4, 8.8) implies that the true there is a 95% confidence that the true parameter value is contained in this interval.

The mistake is that the student concluded that the sample mean is contained in between the interval. This is incorrect because the population is predicted to be contained in the interval.

(c)

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

The 95% confidence interval for the mean rating, (8.4, 8.8) implies that the true mean satisfaction score is contained between 8.4 and 8.8 with probability 0.95 or 95%.

Thus, the students is not making any misinterpretation.

(d)

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

In this case the sample size is,

n = 500 > 30

Thus, a Normal distribution can be applied to approximate the distribution of the alumni ratings.

7 0

3 years ago

Let p=x^2-2 which equation is equivalent to (x^2-2)^2+18=9x^2-18 in terms of p

Bad White [126]

Answer:

The equivalent equation is $p^2 + 18 = 9p$

Step-by-step explanation:

p is given by the following relation:

$p = x^2 - 2$

And we are given the following equation:

$(x^2 - 2)^2 + 18 = 9x^2 - 18$

On the right side, we can simplify. So

$(x^2 - 2)^2 + 18 = 9(x^2 - 2)$

Replacing $x^2 - 2$ by p, the equation is:

$p^2 + 18 = 9p$

6 0

3 years ago

What was Mike's average rate of descent over his last three hours?

Romashka [77]

Answer:

The average rate of descent over the last 3 hours is 1000 ft/h.

Step-by-step explanation:

Rate of Change

It's usually referred to as to the variation that one magnitude has in reference to another. The reference magnitude can be time t. The rate of change is calculated as the slope of the curve that represents the function.

The image shows the variation of Mike's height above sea level in feet with time in hours. We need to calculate the rate of change in the last three hours (from 7 to 10).

The rate of change can be calculated with the slope of the line, which formula is:

$\displaystyle m=\frac{h_2-h_1}{t_2-t_1}$

Let's pick two points (7,4000) (10,1000):

$\displaystyle m=\frac{1000-4000}{10-7}=\frac{-3000}{3}=-1000$

$m=-1000\ ft/h$

Note the rate of change is negative, which means the height is decreasing.

The average rate of descent over the last 3 hours is 1000 ft/h.

8 0

2 years ago

Emily is 46 years old. Colin is 11 years older than Emily. Dan is 5 years younger than Emily. What is the total of their combine

Nonamiya [84]

Answer:

144

Step-by-step explanation:

Data:

Emily's age : 46 years old

Find Colin's age

Colin's age: 11 years older than Emily

Emily's age + 11

46 + 11 = 57 years old

Find Dan's age

Dan's age: 5 years younger than Emily

Emily's age - 5

46 - 5 = 41 years old

Find their combined ages

Combined ages: Emily's age + Colin's age + Dan's age

Combined ages = 46 + 57 + 41

Total = 144

Therefore, the total of their combined ages is 144.

3 0

2 years ago

B. x + 5y = 8 -x + 2y = -1

igomit [66]

Answer:

(3, 1)

Step-by-step explanation:

x+5y=8

-x+2y=-1

-------------

7y=7

y=7/7=1

x+5(1)=8

x+5=8

x=8-5=3

Answer: x=3, y=1.

8 0

2 years ago