Chapter 6 Supplemental Problems PDF

**Chapter 6 -- supplemental problems** 1\. Describe the distribution of sample means (shape, central tendency, and variability) for sample of n = 100 selected from a population with a mean of 40 and a standard deviation of 10. 3\. The distribution of sample means is not always a normal distributio...

**Chapter 6 -- supplemental problems** 1\. Describe the distribution of sample means (shape, central tendency, and variability) for sample of n = 100 selected from a population with a mean of 40 and a standard deviation of 10. 3\. The distribution of sample means is not always a normal distribution. Under what circumstances is it not normal? 5\. For a population with a mean of μ = 70 and σ = 20, how much error, on average, would you expect between the sample mean and the population mean for each of the following sample sizes? a\. n = 4 b\. b = 16 c\. n = 25 7\. For a population with σ = 12, how large a sample is necessary to have a standard error that is: a\. less than 4 points? b\. less than 3 points? c\. less than 2 points? 9\. For a population with μ = 80 and σ = 12, find the z score corresponding to each of the following samples. Then answer: What effect does sample size have on the z score of a sample mean, if everything else is held constant? a\. M = 83 for a sample of n = 4 b\. M = 83 for a sample of n = 16 c\. M = 83 for a sample of n = 36 11\. A normal distribution has a mean of μ = 60 and σ = 18. For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size. a\. M = 67 for n = 4 scores b\. M = 67 for n = 36 scores 13\. The population of IQ scores forms a normal distribution with a mean of μ = 100 and σ = 15. What is the probability of obtaining a sample mean greater than M = 97, a\. for a sample of n = 9 people? b\. for a sample of n = 25 people? 15\. A normal distribution has a mean of μ = 54 and σ = 6. a\. What is the probability of selecting a score less than x = 51? b\. What is the probability of selecting a sample of n = 4 scores with a mean less than M = 51? c\. What is the probability of selecting a sample of n = 36 scores with a mean less than M = 51? 17\. For random samples of n =25 selected from a normal distribution with a mean of m = 50 and s = 20, find each of the following: a\. The range of sample means that defines the middle 95% of the distribution of sample means b\. The range of sample means that defines the middle 90% of the distribution of sample means. (i.e. a 99% confidence interval). 19\. At the end of the spring semester, the Dean of Students sent a survey to the entire first-year class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of μ = 9 pounds with σ = 6. The distribution of scores was approximately normal. A sample of n = 4 students is selected and the average weight change is computer for the sample. a\. What is the probability that the sample mean will be greater than 10 pounds? In other words, b\. Of all the possible samples, what proportion will show an average weight loss? In symbols, c\. What is the probability that the sample mean will be a gain of between M = 9 and M = 12 21\. The average age for licensed drivers in the county is m = 40.3 years with s = 13.2 years. a\. A researcher obtained a random sample of n = 16 parking tickets and computed an average age of M = 38.9 years for the drivers. Computer the z-score for the sample mean and find the probability of obtaining an average age this young or younger for a sample of licensed drivers. b\. The same researcher obtained a sample of n = 36 speeding tickets and computed an average age of M = 36.2 years for the drivers. Compute the z-score for the sample mean and find the probability of obtaining an average age this young or younger for a random sample of licensed drivers. Is it reasonable to conclude that this set of n = 36 people is a representative sample of licensed drivers? **[Chapter 6 answers]** 1\. The distribution of sample means will be normal (because n \> 30), have a mean of μ = 40, and a standard error of σ~M~ = 1. 3\. The distribution of sample means will not be normal when it is based on small samples ( m\ 9 b\. n \> 16 c\. n \> 36 9\. a. σ~M~ = 6 points and z =.5 b\. σ~M~ = 3 points and z = 1.0 c\. σ~M~ = 2 points and z = 1.5 11\. a. With σ~M~ = 9, M = 67 corresponds to z =.78 which is not extreme b\. With σ~M~ = 3, M = 67 corresponds to z = 2.33 which is extreme 13\. a. σ~M~ = 5, z = -.60, and p =.7257 b\. σ~M~ =3, z = - 1.0, and p =.8413 15\. a. z = -.50 and p =.3085 b\. σ~M~ = 3, z = -1.0 and p =.1587 c\. σ~M~ = 1, z = - 3.0 and p =.0013 17\. a. σ~M~ = 4, z ± 1.96 and the range is 42.16 to 57.84 b\. σ~M~ = 4, z ± 2..58 and the range is 39..68 to 60.32 19\. a. z =.33 and p =.3707 b\. p =.3413 21. a. With a standard error of σ~M~ = 3.3. M = 38.9 corresponds to z = -.42 and p =.3372. This is not an unusual sample. It is representative of the population. b\. With a standard error of 2.2, M = 36.2 corresponds to z = -1.86 and p =.0314. The sample mean is unusually small and not representative.