Tuesday

January 24, 2017
Posted by **Tami** on Sunday, June 9, 2013 at 6:09pm.

+5, +6, +3, +1,+8, +5, +4,+4, +3, -1

+2, +7, +1, +5, +8, 0, +4, +6, +5, +3

a) Sketch a histogram showing the distribution of weight-change scores.

b) Calculate the mean weight change score for this sample

c) Does there appear to be a consistent trend in weight change during the semester?

- statistics -
**Tami**, Sunday, June 9, 2013 at 8:04pmDescribe the distribution of sample means (shape, expected value, and standard error) for samples of

n _ 36 selected from a population with a mean of ì _ 100 and a standard deviation of _ _ 12.

The distribution of sample means is not always a normal distribution. Under what circumstances is the

distribution of sample means not normal?

For a population with a mean of ì _ 70 and a standard deviation of _ _ 20, how much error, on average,

would you expect between the sample mean (M) and the population mean for each of the following sample

sizes?

a. n _ 4 scores

b. n _ 16 scores

c. n _ 25 scores

If the population standard deviation is _ _ 8, how large a sample is necessary to have a standard error

that is:

a. less than 4 points?

b. less than 2 points?

c. less than 1 point?

For a population with a mean of ì _ 80 and a standard deviation of _ _ 12, find the z-score corresponding to

each of the following samples.

a. M _ 83 for a sample of n _ 4 scores

b. M _ 83 for a sample of n _ 16 scores

c. M _ 83 for a sample of n _ 36 scores

A population forms a normal distribution with a mean of ì _ 80 and a standard deviation of _ _ 15. 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 _ 84 for n _ 9 scores

b. M _ 84 for n _ 100 scores

The population of IQ scores forms a normal distribution with a mean of ì _ 100 and a standard deviation of _ _ 15. What is the probability of obtaining a sample mean greater than M _ 97,

a. for a random sample of n _ 9 people?

b. for a random sample of n _ 25 people?

A population of scores forms a normal distribution with a mean of ì _ 40 and a standard deviation of _ _ 12.

a. What is the probability of randomly selecting a

score less than X _ 34?

b. What is the probability of selecting a sample of

n _ 9 scores with a mean less than M _ 34?

c. What is the probability of selecting a sample of

n _ 36 scores with a mean less than M _ 34?

At the end of the spring semester, the Dean of Students sent a survey to the entire freshman 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 ì _ 9 pounds with a standard deviation of _ _ 6. The distribution of scores was approximately

normal. A sample of n _ 4 students is selected and the average weight change is computed for the sample.

a. What is the probability that the sample mean will

be greater than M _ 10 pounds? In symbols, what

is p(M 10)?

b. Of all of the possible samples, what proportion will

show an average weight loss? In symbols, what is

p(M 0)?

c. What is the probability that the sample mean will

be a gain of between M _ 9 and M _ 12 pounds?

In symbols, what is p(9 M 12)?

The average age for licensed drivers in the county is ì _ 40.3 years with a standard deviation of _ _ 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. 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 _ 16

people is a representative sample of licensed

drivers?

b. The same researcher obtained a random 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?

Welsh, Davis, Burke, and Williams (2002) conducted a study to evaluate the effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance. Experienced athletes were given either a carbohydrate-electrolyte drink or a placebo while they were tested on a series of high-intensity exercises. One measure was how much time it took

for the athletes to run to fatigue. Data similar to the results obtained in the study are shown in the following table.

Time to Run to Fatigue (in minutes) Mean SE Placebo 21.7 2.2 Carbohydrate-electrolyte 28.6 2.7

a. Construct a bar graph that incorporates all of the

information in the table.

b. Looking at your graph, do you think that the

carbohydrate-electrolyte drink helps performance?