Variables on both sides 4x + 9 = 2x + 13

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

A magician charges parties a $30 fee to cover travel and miscellaneous expenses plus $19.99 per hour. What an equation for that?

myrzilka [38]

Answer:

30 + 19.99 per hour

Step-by-step explanation:

ADD THEM IN A EQUATION.

SO SIMPLE TO DO THAT!

7 0

3 years ago

Read 2 more answers

Let’s now add x to both sides of the equation and consider the new equation x squared+5+x=11

irina1246 [14]

Answer:x=3

Step-by-step explanation:x squared is one x.you then add the X's to get 2x.then you subtract the five on the other side to get 2x=6.after you get that you divide both sides by 2 to get x=3

3 0

3 years ago

When adding vegetables to a footlong (30 cm) sandwich, how many ounces or slices of vegetables do you use? select all that apply

MA_775_DIABLO [31]

A footlong sandwich will fit other ingredients besides vegetables, such as 4 slices cheese or 4 strips of beacon, but if we only talk about vegetables, you can 1.5 oz. Lettuce and 1 oz. Onion, 6 slices each; Tomato, cucumber, pickles, pepper, olives, jalapeños.

7 0

3 years ago

Given a scalene triangle with whole number angle measurements, what is the greatest sum possible of the two smallest angles?

Olegator [25]

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define scalene triangle

A Scalene Triangle is any triangle with unequal sides. This means that, in a scalene triangle, all of the three sides and angles are different lengths, just like in the illustration below. This also means that each angle has to be different.

STEP 2: Get the greatest sum possible of the two smallest angles

Since the measures of the angles of the triangle are different whole numbers , for the sum of the two angles to be the least possible, one of the angles must be smallest whole number i.e 1°

Now, the next smallest angle will be the next angle of a whole number that is not 1 degree, i.e, 2 degrees.

Thus, the greatest possible sum of the measures of two smallest angles will be:

$1^{\circ}+2^{\circ}=3^{\circ}$

Hence, the greatest sum possible of the two smallest angles is 3 degrees

7 0

1 year ago