# One question in the survey asked how much time per year the children spent in volunteer activities. The sample mean was 14.76 hours and the sample standard deviation was 16.54 hours.Required:a. Based on the reported sample mean and sample standard deviation, explain why it is not reasonable to think that the distribution of volunteer times for the population of South Korean middle school students is approximately normal. b. The sample size was not given in the paper, but the sample size was described as large. Suppose that the sample size was 500. Explain why it is reasonable to use a one-sample t confidence interval to estimate the population mean even though the population distribution is not approximately normal. c. Calculate and interpret a confidence interval for the mean number of hours spent in volunteer activities per year for South Korean middle school children.

a. If the distribution was normal, many values would be negative, what is incompatible with the response variable (hours dedicated to volunteer activities).

b. If the sample is big, accordingly to the Central Limit Theorem, the sampling distribution shape tends to be normally-like, so we can apply a one-sample t-test.

c. The 95% confidence interval for the mean is (13.307, 16.213).

Step-by-step explanation:

a. If the distribution was normal, the values with one or more standard deviation below the mean would be negative, what is incoherent for this case. This, in a normal distribution, represents approximately 16% of the values.

If we calculate the probabilty for a normal distribution with the sample parameters, the probability of having "negative hours" is 18.6% (see picture attached).

b. If the sample is big, accordingly to the Central Limit Theorem, the sampling distribution shape tends to be normally-like, so we can apply a one-sample t-test.

The sampling distribution standard deviation is also reduced by a factor of 1/√n.

c. We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=14.76.

The sample size is N=500.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

The t-value for a 95% confidence interval is t=1.965.

The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 95% confidence interval for the mean is (13.307, 16.213).

## Related Questions

you need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x-3y=12 and -2x+y=8

Sorry this is so late.

The answer is "Add the left side of equation 2 to the left side of equation 1"

bro!! I'm on the same question on ap3x!!

lol

Step-by-step explanation:

What is the volume of 22.5 g of metal with a density of 2.81 g/cm

Answer:V = 72.1 cm³ - 50.0 cm³ = 22.1 cm³

D = mV=99.7g22.1cm³ = 4.51 g/cm³

Step-by-step explanation:

d = mV

m = d×V

V = md

DENSITY

Density is defined as mass per unit volume.

d = mV

Example:

A brick of salt measuring 10.0 cm x 10.0 cm x 2.00 cm has a mass of 433 g. What is its density?

Step 1: Calculate the volume

V = lwh = 10.0 cm × 10.0 cm × 2.00 cm = 200 cm³

Step 2: Calculate the density

d = mV = 433g200cm³ = 2.16 g/cm³

MASS

d = mV

We can rearrange this to get the expression for the mass.

m = d×V

Example:

If 500 mL of a liquid has a density of 1.11 g/mL, what is its mass?

m = d×V = 500 mL × 1.11g1mL = 555 g

VOLUME

d = mV

We can rearrange this to get the expression for the volume.

V = md

Example:

What is the volume of a bar of gold that has a mass of 14.83 kg. The density of gold is 19.32 g/cm³.

Step 1: Convert kilograms to grams.

14.83 kg × 1000g1kg = 14 830 g

Step 2: Calculate the volume.

V = md = 14 830 g × 1cm³19.32g = 767.6 cm³

Root 25-2(3+4*(-2)) whole square​

-45.

Step-by-step explanation:

I am assuming you mean

√25 - 2(3 +4(-2))^2

= 5 - 2(3-8)^2

= 5 - 2 * (-5)^2

= 5 - 2*25

= -45.

Write an equation in point-slope from for a line that passes through the given set of points. (3,5) and (-6,-4)

y-y1=m(x-x1)

does this help or do you need help plugging in and finding slope?

The graph of a quadratic function is shown above.According to the fundamental theorem of algebra, the function above has [___] real zeros and [___] complex zeros.

• 0 real zeros
• 2 complex zeros

Step-by-step explanation:

The "fundamental theorem of algebra" says a polynomial of degree n will have n zeros. If the polynomial has real coefficients, the complex zeros will appear in conjugate pairs.

The graph of this quadratic (degree = 2) does not cross the x-axis, so there are no real values of x that make y=0. That means the two zeros are both complex.

1) A 15 foot flagpole casts an 11 foot shadow. At the exact same time a 28 foot tree casts a shadow. Which proportion would correctly find the length of the tree's shadow? A) x 28 = 11 15 B) x 28 = 15 11 C) 28 x = 11 15 D) x 15 = 11 28

D

The model involves similar triangles with the ratios of corresponding sides being equal

let x be the length of the tree's shadow, then

= ( cross- multiply )

15x = 11 × 28