# Mathematics

 Question 1 0 / 20 points

David Lane: Page 364     Exercise 4

Is a 99% confidence interval wider than a 95% confidence interval?

Question options:

 Yes.  In order to be more confident that an interval contains the true population mean you must increase the confidence interval width. No.  The width of a confidence interval depends on two controllable parameters, the sample size (n) and the confidence level (z or t).  You can increase the confidence level and maintain the same interval width by increasing the sample size by an appropriate mount. No.  Confidence level and Confidence width are independent of each other and there is no relationship between the confidence level and the confidence width. Question 2 0 / 20 points

Illowsky: Page 450     Exercise 100

What is meant by the term “90% confident” when constructing a confidence interval for a mean?

Question options:

 If we took repeated samples, approximately 90% of the samples would produce the same confidence interval. If we took repeated samples, approximately 90% of the confidence intervals calculated would contain the sample mean. If we took repeated samples, approximately 90% of the confidence intervals calculated would contain the true value of the population mean. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples. Question 3 0 / 20 points

David Lane: Page 365     Exercise 15

You take a sample of 22 from a population of test scores.  The mean of your sample is 60 and the population standard deviation is 10.

What is the point estimate for the population mean?

________

What is the 99% confidence interval for the population mean?

Enter the lower number of the conference interval for the first number and the upper number of the conference interval for the second number.

Enter each number rounded to 1 decimal place.

________

________

Assume you do not know the population standard deviation.  The sample standard deviation is 10.  What is the new 99% confidence interval on the mean?

Enter the lower number of the conference interval for the first number and the upper number of the conference interval for the second number.

Enter each answer rounded to 1 decimal place.

________

________

What distribution did you use when computing the first confidence interval?

What is the degrees freedom for calculating the confidence interval?

Answer the question by selecting the proper letter a, b, c or d.

Enter 0 for the degrees freedom if degrees freedom is no applicable for the distribution being used.

a    The Normal distribution

b    The t distribution

c    The Uniform distribution

d    Neither of the above distributions

________

________

What distribution did you use when computing the second confidence interval?

What is the degrees freedom for calculating the confidence interval?

Answer the question by selecting the proper letter a, b, c or d.

Enter 0 for the degrees freedom if degrees freedom is no applicable for the distribution being used.

a    The Normal distribution

b    The t distribution

c    The Uniform distribution

d    Neither of the above distributions

________

________

 Question 4 0 / 20 points

David Lane: Page 366     Exercise 18

You were interested in how long the average psychology major at your college studies per night, so you asked 10 psychology majors to tell you the amount time they study.

You were given the following ‘study times’: 2, 1.5,   3, 2, 3.5, 1, 0.5, 3, 2, 4.

The average study time from the above data (Xbar) is 2.25
The standard deviation of the ‘study times’ from the above data is 1.11

(You should be able to verify the mean and standard deviation of the above data by using an appropriate formulas and/or an Excel spreadsheet.)

What is the appropriate distribution for finding a confidence interval?

Select the correct answer and enter the appropriate letter.

A     Uniform distribution

B     Normal distribution

C     t distribution

D     Chi Square distribution

________

What is the degrees of freedom (dF)?

If the question is inappropriate for the distribution selected enter the number 0.

________

Find a 95% confidence interval on the population mean.

Enter the lower number for the confidence interval first and the upper number for the confidence interval next.

Enter each number rounded to 2 decimal places.

________

________

Find a 90% confidence interval for the population mean.

Enter the lower number for the confidence interval first and the upper number for the confidence next.

Enter each number rounded to 2 decimal places.

________

________

 Question 5 0 / 20 points

David Lane: Page 365    Exercise 12

A person claims to be able to predict the outcome of flipping a coin.  The person is correct 16 out of 25 times.  Answer the following questions based upon the above experiment.

What is the point estimate for the proportion of times the person predicted the coin flips correctly?

Enter answer as a fraction or a 2 place decimal with a zero to the left of the decimal point.  Do not enter your answer in percent.

________

What is the sample size being used for calculating a confidence interval for the proportion of heads demonstrated base upon the reported data?

________

Compute a 95% confidence interval for the proportion of times the person predicted the coin flips correctly.

Enter the lower number and the upper number for the confidence interval with the lower number first.

Enter answer as a decimal rounded to 3 decimal places with a zero to the left of the decimal point.

________

________

What conclusion can you draw from the confidence interval about the ability of the person to predict the outcome of a coin flip?

Select the correct answer and enter the letter that is associated with that answer.

A     Based upon the data, the calculated conference interval supports the claim that the person flipping the coins can predict the outcomes.

B     Based upon the data, the calculated conference interval does not support the claim that the person flipping the coins can predict the outcomes.

C     There is insufficient information to draw any conclusion from the experimental results

________

What number must the lower number in the confidence interval exceed in order for the confidence interval to support the claim of being able to predict the outcome of flipping a coin?

Enter answer to 1 decimal place with a 0 to the left of the decimal point.

________

Extra Credit:

95. Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches.

a.

i. x ¯ =________

ii. σ =________

iii. n =________

b. In words, define the random variables X and X ¯ .

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean height of male Swedes.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

99. A camp director is interested in the mean number of letters each child sends during his or her camp session. The population standard deviation is known to be 2.5. A survey of 20 campers is taken. The mean from the sample is 7.9 with a sample standard deviation of 2.8.

a.

i. x ¯ =________

ii. σ =________

iii. n =________

b. Define the random variables X and X ¯ in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 90% confidence interval for the population mean number of letters campers send home.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. What will happen to the error bound and confidence interval if 500 campers are surveyed? Why?

100. What is meant by the term “90% confident” when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.

c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

111. Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats.

a.

i. x ¯ = __________

ii. sx = __________

iii. n = __________

iv. n-1 = __________

b. Define the random variables X and X ¯ in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 92% confidence interval for the population mean number of unoccupied seats per flight.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

119. According to a recent survey of 1,200 people, 61% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job.

a. Define the random variables X and P′ in words.

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 90% confidence interval for the population proportion of people who feel the president is doing an acceptable job.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

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