# statistics

posted by .

A nutritionist studying weight gain for college freshmen obtains a sample of n = 20 first year student at the state college. Each student is weighed on the first day of school an again on the last day of the semester. The following scores measure the change in weight, in pounds, for each student. A positive score indicates a weight gain during the semester.
+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 -

Describe 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?

## Similar Questions

1. ### Algebra

The school that Trevon goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 12 adult tickets and 4 student tickets for a total of \$188. The school took in \$171 on the second day by selling …
2. ### college math

15. Records at a high school indicate that each year for the past five years, 120 of the 1,500 students were absent on the first day of hunting season. What is the likelihood that a particular student will be absent on the first day …
3. ### Science

A student observed the apparent shape of the moon every night for a period of 60 days. On Day 10 the student observed a full moon. On which day did the student most likely observe a full moon?
4. ### STATISTICS

Suppose that, for students who are enrolled in college algebra, 78 percent are freshmen, 40 percent are female, and 28 percent are female and are freshmen. Your answers below should be entered as decimals and rounded to three decimal …
5. ### math

a school is divided into 4 houses,P,Q,R and S.On sports day,the students line up so that a student from P is first in line,then a student from Q then a student from R then a student from S,then a student from P and so on with same …
6. ### MATH

A SCHOOL IS DIVIDED INTO 4 HOUSES P,Q,R,S. ON SPORTS DAY,STUDENTS LINE UP SO THAT A STUDENT FROM P IS FIRST IN LINE,THEN A STUDENT FROM Q THEN A STUDENT FROM R THEN A STUDENT FROM S THEN A STUDENT FROM P AND SO ON WITH SAME ORDER REPEATING …
7. ### Algebra

the table shows the results of a survey of college students. find the probability that a student's first class of the day is a humanities class, given the student is female. First class of the day for college students male female humanities …
8. ### statistics

The time a student spends in the shower on any school day is an exponential random variable with a mean of 298 seconds. a)What is the probability that the student spends more than 310 seconds in the shower on one day?
9. ### Algebra

Help? The school john goes to is selling tickets to the annual dance competition . On the first day of sales the school sold 2 senior citizen tickets and 13 student tickets for a total of \$108. The school took in\$144 on the second
10. ### Math

Every few days a student at a school will receive a souvenir such as a pencil or shirt. Every 24th day a student receives a souvenier. Every 56th day a student receives a souveiner and every 64th day a student receives a souvenier. …

More Similar Questions