Math 156–Sat: HW #4 Name:
1. What is the difference between [pic] and[pic]? Between s and[pic]? (10 points)
2. Explain the difference between [pic] and [pic] and between [pic] and[pic]? (10 points)
3. Suppose that a random sample of size 64 is to be selected from a population having [pic] and standard deviation 5.
(a) What are the mean and standard deviation of the [pic] sampling distribution? Can we say that the shape of the distribution is approximately normal? Why or why not? (10 points)
(b) What is the probability that [pic] will be within 0.5 of the population mean? (5 points)
(c) What is the probability that [pic] will differ from the population mean by more than
…show more content…
medical residents who have credit card debt of more than $3000. (10 points)
(c) How many medical residents should be sampled in order to build a 99% confidence interval with an error of no more than 4%? (5 points)
10. The airborne times of United Airlines flight 448 from Albuquerque to Denver on 10 randomly selected days are shown below. You may assume that the flight times of all such flights are normally distributed. (10 points each)
57 54 55 51 56 48 52 51 59 59
(a) Find a 90% confidence interval for the mean airborne time for flight 448.
(b) Repeat part (a) if it is known that the standard deviation of such flights is 1.7 minutes.
11. The eating habits of 12 bats were examined in the article “Foraging Behavior of the Indian False Vampire Bat” (Biotropica [1991]). For these 12 bats, the mean time to consume a frog was [pic] minutes and the standard deviation was 7.7 minutes. Construct a 90% confidence interval for the mean time it takes this bat to consume a frog. What assumption(s) must be made here? (10 points)
Math 156–Sat: HW #4 - Solutions
1. [pic] is the mean of a sample whereas [pic] is the mean for the entire population
s is the standard deviation of a sample whereas [pic] is the standard deviation of the entire population
2. [pic] is the mean for the entire population whereas [pic] is the mean of the
2) Compute the standard deviation for each of the four samples. Does the assumption of .21 for the population standard deviation appear reasonable?
So, we have a distribution with a mean of 20,000 and a standard deviation of 5,102.
Standard deviation is important in comparing two different sets of data that has the same mean score. One standard deviation may be small (1.85), where the other standard deviation score could be quite large (10)(Rumsey,
2. In order to determine the average amount spent in November on Amazon.com a random sample of 144 Amazon accounts were selected. The sample mean amount spent in November was $250 with a standard deviation of $25. Assuming that the population standard deviation is unknown, what is a 95% confidence interval for the population mean amount spent on Amazon.com in November?
(a) Then mean of the sample and the value of Z with an area of 10% in right tail.
5. Give the standard deviation for the mean and median column. Compare these and be sure to identify which has the least variability?
and SD are _______________________ statistics. The mean is the measure of Central tendency of a distribution while SD is a measure of dispersion of its scores. Both X and SD is descriptive statistics.
Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.
12. _____ For a given population, confidence intervals constructed from larger samples tend to be narrower than those constructed from smaller samples. Which statement below best describes why this is true? (A) The variability of the sample mean is less for larger samples. (B) The z-value for larger samples tends to be more accurate. (C) The population variance is larger for large populations. (D) As the sample size increases, the z-value (or t-value) becomes smaller. A machine dispenses potato chips into bags that are advertised as containing one pound of product. To be on the safe side, the machine is supposed to be calibrated to dispense 16.07 ounces per bag, and from long time observation, the distribution of the fill-weights is known to be approximately normal and the process is known to have a standard deviation of 0.15 ounces.
Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 30 people is picked from population A, and random sample of 50 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why? Despite, both Population A and Population having a mean height of 70.0 inches with an SD of 6.0, Population B will
standard deviation standardized value rescaling z-score normal model parameter statistic standard Normal model 68-95-99.7 Rule normal probability plot
2. For the following set of scores, fill in the cells. The mean is 74.13 and the standard deviation is 9.98.
Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of
We first find zc for the 98% confidence interval. Consulting the table above we find it to be -2.33. Also [pic]