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Statistics : Standard Deviation and Mean (10 Problems)

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1. True or False?
The standard deviation of a population will always be smaller than the standard deviation of the sample means (of the samples used to estimate this same population).

2. The mean height for a population is 65 inches and the standard deviation is 3 inches. Let X_ denote the mean height for a sample of people picked randomly from the population. The standard
deviation of X_ for samples of size 30 is ________ the standard deviation of X_ for samples of size 20?
a. greater than
b. less than
c. equal to
d. impossible to tell
3. The error which results from using a sample to estimate a population characteristic is called the ___________.
a. rounding error
b. sampling error
c. statistical error
d. error interval

5. The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B denote the events described below.
Event A: The mean height of a random sample of 16 people will be within 1 inch of the population mean.
Event B: The mean height of a random sample of 50 people will be within 1 inch of the population mean.
a. The probability of event A is greater than the probability of event B
b. The probability of event B is greater than the probability of event A
c. The probability of event A is equal to the probability of event B
d. The probability of event A is unrelated to the probability of event B

7. When using sample means to estimate a population mean, increasing the size of the sample will result in:
a. smaller sampling error and OX will decrease.
b. smaller sampling error and OX will increase.
c. greater sampling error and OX will decrease.
d.greater sampling error and OX will increase
8. The mean price of a new mobile home is $43800. The standard deviation of the price is $7200. Let X_ denote the mean price of a sample of new mobile homes. For samples of size 50, find the mean price.
Use only numbers in your answer. Do not use a dollar sign, do not use a comma, do not use a decimal point, and do not write any words, such as "dollars".
9. The mean price of a new mobile home is $43800. The standard deviation of the price is $7200. Let X_ denote the mean price of a sample of new mobile homes. For samples of size 50, find the standard deviation of
of X_. Round to the nearest cent (two decimal places). Use only numbers and a decimal point in your answer. Do not use a dollar sign, do not use a comma, and do not write any words, such as "dollars".
10. The table reports the distribution of pocket money, in bills, of the 6 students in a statistics seminar.
Student Bridgette Timothy Aaron Barry Lucille Stacey
Dollars 2 4 4 5 5 7
For a random sample of size two, find the probability that the sample mean will be within $1 of the population mean. Round to the nearest three decimal places.
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(See attached file for full problem description)

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Solution Summary

Ten problems involving Standard Deviation and Mean are solved.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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