Question

Chapter 7 hand-in Homework
1) Mention three thing about the standard error of the mean

2) Why is the Central Limit Theorem important in statistics?

3) The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of nine tennis balls, 
a) What is the sampling distribution of the mean?   

b) Assume the diameter of a brand of tennis balls was known to have a right skewed distribution with a mean of 2.63 inches and a standard deviation of 0.03 inch. Suppose we collect a random sample of 100 tennis balls. Describe the sampling distribution of the mean diameter for these 100 tennis balls.

c) How will the mean of the sampling distribution compare to the population mean in this problem?

d) How will the standard deviation of the sampling distribution (standard error of the mean) compare to the population standard deviation?

e) Find the approximate probability that the mean diameter of nine tennis balls exceeded 2.61.

f) Find the approximate probability that the mean diameter of the nine tennis balls exceeded 2.68.

g) Find the approximate probability that the mean diameter of the nine tennis balls was no more than 2.60 inches.

4) n a random sample of 64 people, 48 are classified as “successful”.
a) Determine the sample proportion, p, of “successful” people.

b) Determine the standard error of the proportion.

c) What proportion of the samples will have between 20% and 30% of people who will considered “successful”?

d) What proportion of the samples will have less than 75% of people who will be considered “successful”?

e) 90% of the samples will have less than what percentage of people who will be considered “successful”?

f) 90% of the samples will have more than what percentage of people who will be considered “successful”?

Answer 1

3)

Here we have

(a)

Sample size: n=9

The sampling distribution of sample mean will be approximately normal distribution with mean

and standard deviation is

(b)

Sample size: n=100

Since sample size is greater than 30 so sampling distribution of sample mean will be approximately normal distribution with mean

and standard deviation is

(c)

The mean of the sampling distribution is equal to the population mean.

(d)

The standard deviation of the sampling distribution (standard error of the mean) is smaller than the population standard deviation.

(e)

The z-score for is

Using z table, the probability that the mean diameter of nine tennis balls exceeded 2.61 is

(f)

The z-score for is

Using z table, the probability that the mean diameter of nine tennis balls exceeded 2.68 is

(g)

The z-score for is

Using z table, the the approximate probability that the mean diameter of the nine tennis balls was no more than 2.60 inches is