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Homework Assignment #7 – Intro to Statistics – MTH115 – Spring 2014

Please staple these pages together – I will deduct 2 pts if not stapled when turned in

1. (4 points) Answer the following questions regarding confidence level, margin of error,

standard deviation and sample size for estimating the population mean. Use the relationship

amongst these values:

For a given confidence level = ( 1 – α ). The margin of error (E) is given as:

E ï€½ ï‚± zï¡ /2

ïƒ—ï³ / n (assuming the population standard deviation is known).

(a) If the confidence level is decreased (which means α gets larger), what happens to

the value of zα/2? Does the margin of error get larger or smaller?

(b) If the sample size is decreased, what happens to the margin of error?

(c) Is the standard deviation of the distribution of sample means always larger or smaller

than the population standard deviation and why?

2. (4 points) A study of 31 professors showed the sample mean time to correct a paper was

20.2 minutes. The population standard deviation is 8.2 minutes. What is the point estimate

of the population mean and what is the 90% confidence interval? What is the margin of

error? Did you use ZInterval or TInterval for this problem?

Provide all of the following:

Point Estimate: _____________

90% Confidence Interval: ________________

Margin of Error: _____________

Use ZInterval or TInterval: (circle which one you used)

3. (4 points) Find the 95% confidence interval for the population mean for the list of sample

data shown below. The population standard deviation is 8.4. Write down whether you use

ZInterval or TInterval for this problem. Test for outliers and remove any outliers from the

sample before calculating the confidence interval. Assume the population (from which this

sample was taken) is normally distributed.

37 39 40 44 54 57 58 58

59 62 64 65 70 75 83

For all questions, in addition to your answer, please

write down what you entered into your calculator. Homework Assignment #7 – Intro to Statistics – MTH115 – Spring 2014

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4. (4 points) Travel distance to work for a sample of 33 people had a sample mean of 28.2

miles and a sample standard deviation of 7.1 miles. What is the 99% confidence interval for

the population mean? Write down whether you use ZInterval or TInterval for this problem.

5. (4 points) Find the 95% confidence interval for the population mean for the list of sample

data shown below. Write down whether you use ZInterval or TInterval for this problem.

Test for outliers and remove any outliers from the sample before calculating the confidence

interval. Assume the population (from which this sample was taken) is normally distributed.

20 24 27 33 35 37 39

42 43 45 46 57 70

6. (4 points) The population standard deviation for gas mileage for a certain model of car is

known to be 1.8 miles per gallon. How many cars would you have to test (what sample size

would you need) to get a margin of error of 0.5 mile per gallon (or less) for the population

mean at a 90% confidence level?

7. (4 points) In a survey of 720 people, 320 of them were in favor of building a new skate park

in Forest Park. What is the 95% confidence interval for the population proportion of people

who are in favor of building the new park? What is the margin of error? Do the test to see

if the sample is large enough to use the normal approximation. Round all of your

answers in percent to the nearest tenth of a percent.

Homework Assignment #7 – Intro to Statistics – MTH115 – Spring 2014

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8. (4 points) How many people would you need to survey to get a margin of error of 2%

(±0.02) or less at a 90% confidence level for the population proportion of people with red

hair if the estimate for people with red hair in the population is 28%? Remember to round

UP to the next highest integer.

How many people would you need to survey if you do NOT have an estimate of the

population proportion of red-haired people? Remember to round UP to the next highest

integer.

9. (4 points) In a survey of 920 people, 65% of them had sent a text message at least once in

the last six months. What is the 95% confidence interval for the population proportion of

people have sent a text message in the last six months? Do the test to see if the sample is

large enough to use the normal approximation. Round all of your answers in percent to

the nearest tenth of a percent.

10. (4 points) A random sample of 41 students had an average SAT score of 1500 and a sample

standard deviation of 360. Assume the population is normally distributed. What is the 90%

confidence interval for the population standard deviation (σ)?

Subject | Mathematics |

Due By (Pacific Time) | 04/02/2014 12:00 am |

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