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
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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. 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?
5. Give the standard deviation for the mean and median column. Compare these and be sure to identify which has the least variability?
A business wants to estimate the true mean annual income of its customers. It randomly samples 220 of its customers. The mean annual income was $61,400 with a standard deviation of $2,200. Find a 95% confidence interval for the true mean annual income of the business’ customers.
7. The mean (X—) is a measure of ____________ ______________ of a distribution while the SD is a measure
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
(b) The value of Z with an area of 5% in the right tail, but not the sample mean.
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
5. When is it more appropriate to use the median as a measure of center rather than the mean? Why?
Topics Distribution of the sample mean. Central Limit Theorem. Confidence intervals for a population mean. Confidence intervals for a population proportion. Sample size for a given confidence level and margin of error (proportions). Poll articles. Hypotheses tests for a mean, and differences in means (independent and paired samples). Sample size and power of a test. Type I and Type II errors. You will be given a table of normal probabilities. You may wish to be familiar with the follow formulae and their application.
normally distributed, the 95% of all values will be within 2 standard deviations from the mean.
2. For the following set of scores, fill in the cells. The mean is 74.13 and the standard deviation is 9.98.
Mean is the average of a group of scores (Woolfolk, 2014). Mean and average are used interchangeably. To find the mean, a teacher will add all of the scores together and divided by the number of tests. For example, a teacher wants to find the mean of the spelling test, the spelling test scores are as the following, 10, 8, 7, 8, 10, 10, 6, 5, 7, and 5. The first step is to add all of the scores together (76). The second step is to divided by the number of tests (10), the quotient is the mean (7.6). The first math equation is 10+8+7+8+10+10+6+5+7+5=76. The second math equation is 76/10=7.6. 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.