Problem Set AP REVIEW ASSIGNMENT #8 …statsanswers.weebly.com/uploads/5/0/8/9/50891699/assistments_8.pdf · Problem Set "AP REVIEW ASSIGNMENT #8" id:[PSABTP9] Select All 1) Problem

Problem Set "AP REVIEW ASSIGNMENT #8" id:[PSABTP9]

Select All

1) Problem #PRAKBZK "PRAKBZK - 269771 - The following dat..."

A) The following dataset is an example of:

© STATS4STEM.ORG

Multiple choice:

Linear Growth

Exponential Growth

Exponential Decay

Power Law

B) The following is an example of exponential growth:

Determine A. Round answer to the nearest hundredth.

Algebra:

42.88

42.875

42.87

Hints:

12.25/3.50 = 3.5

Therefore,

A/12.25 = 3.5

A/12.25 = 3.5

Therefore, A = 3.5 × 12.25 = 42.875 or 42.88 (ROUNDED)

2) Problem #PRAJBJT "PRAJBJT - 31-1-B"

Assistment - Printing Content https://www.assistments.org/build/print/assignment/1034341?mode=deb...

1 of 13 5/2/2014 12:27 PM

What month has the least variablity? State the number or the month in the answer.

© STATS4STEM.ORG

Multiple choice:

5

6

7

8

9

Hints:

Look at the smallest box

type 7

3) Problem #PRAJBPQ "PRAJBPQ - 239674 - Suppose that Kraf..."

Suppose that Kraft’s bags of shredded cheddar cheese are normally distributed with µ = 24 ounces

and σ =3 ounces. If Kraft wants to change the standard deviation so that 5% of the bags weigh less

than 20 ounces, what would the new standard deviation become? Round answer to the nearest

hundreth.

Link to z-table.

© STATS4STEM.ORG

Algebra:

2.44

2.42

2.43

Hints:

Find z that corresponds to an area of 0.05

5% = 0.05 --> z = -1.64

Recall:


2 of 13 5/2/2014 12:27 PM

-1.64 = (20-24)/σ

σ = (20-24)/-1.64

σ = 2.44

4) Problem #PRAJ9XA "PRAJ9XA - 267778 - Using the compute..."

A) Using the computer output for linear regression found below, what percentage of variability in y can be

explained by the linear model where x is the explanatory variable? Round percentage to the nearest

whole number.

© STATS4STEM.ORG

Algebra:

1

1.27

1.3

1%

1 %

Hints:

Click here for STATS4STEM help page.

Multiple R-squared = r2

r2 = 1.27 or 1 (ROUNED)

B) For linear regression, degrees of freedom equals:

Multiple choice:

n

n-1

n-2

n-3

n-4

C) Calculate the margin of error needed to construct a 99% confidence interval for the true slope of the

least-squares regression line. Round answer to the nearest hundredth.


3 of 13 5/2/2014 12:27 PM

Link to t-table.

Algebra:

0.67

0.68

Hints:

Click here for STATS4STEM help page.

margin of error = t* × SEb

margin of error = 0.2013*3.355 = 0.6753 or 0.68 (ROUNDED)

5) Problem #PRAJBUZ "PRAJBUZ - Baseball"

In order for a baseball to pass inspection it must weigh 5 ounces. There is a 2% chance that any

one ball fails inspection. If 127 balls were sent for inspection, what is the probability that at least 1

will fail inspection? Round answer to the nearest hundredths.

© STATS4STEM.ORG

Algebra:

.92

.92314

round to hundreths

0

92

Hints:

P(@least 1) = 1 - P(None)

P(FAIL) = .02 P(PASS) = 0.98

P(@least 1 FAILURE)= 1 - P(NO FAILURES) = 1 - P(ALL PASS)

P(ALL 127 PASS) = 0.98127

P(@least 1 FAILURE)= 1 - P(NO FAILURES) = 1 - P(ALL PASS) = 1 - 0.98127 = 0.9231 OR .92

(ROUNDED)

Type .92

6) Problem #PRAJBX2 "PRAJBX2 - 239932 - &n..."


4 of 13 5/2/2014 12:27 PM

A)

The above figure is a density curve that represents the distribution of random variable X. What is the height

of the density curve? Round answer to the nearest hundredth.

© STATS4STEM.ORG

Algebra:

0.5

1

No, the area under the density curve must equal 1.

Hints:

The area under the density curve must equal 1.

The area of the rectangle is length*height

The length is 9.0 - 7 or 2

2 * Height = 1

Solve for Height

Height = 1/2 = 0.5

B) What is the probability that X is between 7.8 and 8.6? Round answer to the nearest hundredth.

Algebra:

0.4

Hints:

P(7.8 < X < 8.6) = AREA UNDER THE DENSITY CURVE BETWEEN 7.8 and 8.6

AREA = LENGTH * HEIGHT

LENGTH = 8.6 - 7.8= 0.8

HEIGHT = 0.5

AREA = LENGTH * HEIGHT = 0.8 * 0.5 = 0.4

Remember, area equals probability, thus the probability equals 0.4.

C) What is the probability that X=7.4? Round answer to the nearest hundredth.

Algebra:

0

Hints:

P(X=ANY ONE NUMBER)=0

P(X=7.4)=0

D) What is the probability that X is between 8.5 and 8.9 ? Round answer to the nearest hundredth.

Algebra:


5 of 13 5/2/2014 12:27 PM

0.20

Hints:



LENGTH = 8.9-8.5=0.4

HEIGHT = 0.5



E) What is the probability that X is between 8.2 and 9.2? Round answer to the nearest hundredth

Algebra:

0.4

0.5

There is no area between 9.0 and 9.2.

Hints:


Observe, the area under the density curve between 9.0 and 9.2 equals 0.


LENGTH = 8.2-9.0=0.8

HEIGHT = 0.5



7) Problem #PRAJBZS "PRAJBZS - 239986 - You flip a fair c..."

You flip a fair coin 25 times. What is the probability of getting exactly 14 tails? Round answer to the

nearest hundredth.

© STATS4STEM.ORG

Algebra:

0.13

13

Hints:

P(x=14)

Enter in TI-83:

binompdf(25,0.5,14)

Answer: 0.13 or 13%

8) Problem #PRAE8Z7 "PRAE8Z7 - 147743 - Which statement i..."

Which statement is correct?

© STATS4STEM.ORG

Multiple choice:


6 of 13 5/2/2014 12:27 PM

Parameters are always easy to calculate and determine.

No, parameters require information from the entire population which may be costly, difficult, or

impossible to get.

Statistics are often used to estimate the parameter of the population.

A parameter is used to estimate a statistic.

A statistic is used to estimate an unknown parameter.

The population mean is a statistic.

The population mean is a parameter.

The sample mean is a parameter.

The sample mean is a statistic.

9) Problem #PRAE82A "PRAE82A - 147746 - Which statement i..."

Which statement is correct?

© STATS4STEM.ORG

Multiple choice:

Parameters are always easy to calculate and determine.

No, parameters require information from the entire population which may be costly, difficult, or

impossible to get.

A great way to remember statistics are calculated from samples is to remember both statistic and

sample start with the letter S.

A parameter is used to estimate a statistic.

A statistic is used to estimate an unknown parameter.

The population mean is a statistic.

The population mean is a parameter.

The sample mean is a parameter.

The sample mean is a statistic.

10) Problem #PRAH9TA "PRAH9TA - 237863 - Hypothesis Test - 1 Sample Mean - EJS"

A) Bottles of a particular brand of water is supposed to have 300 milliliters (mL) of nutrients. The amount

varies from bottle to bottle because the precision of the machines is not too precise. The distribution is

normal with a standard deviation σ = 3 mL. An inspector of the company suspects that the company is

under-filling the bottles. The inspector took a sample of six bottles and the results are below in an effort to

confirm his suspicion.

299.4, 297.7, 301, 298.9, 300.2, 297

What is the mean of this sample data set? Round answer to the nearest hundredths.

© STATS4STEM.ORG

Algebra:

299.03

Hints:

Rweb:> x=c(299.4, 297.7, 301, 298.9, 300.2, 297)

Rweb:> xbar=mean(x)

Rweb:> xbar


7 of 13 5/2/2014 12:27 PM

[1] 299.0333

Answer is 299.03 (ROUNDED)

B) When conducting a hypothesis test, what is the first thing that we should assume?

Multiple choice:

The Null Hypothesis is true

The Alternative Hypothesis is true

The Null Hypothesis is wrong

The Alternative Hypothesis is wrong

C) For this problem, what would be considered the alternative hypothesis?

A) Ha: µ < 299.03

B) Ha: µ > 299.03

C) Ha: µ < 300

D) Ha: µ > 300

E) Ha: x-bar < 300

F) Ha: x-bar > 300

G) Ha: x-bar < 299.03

H) Ha: x-bar > 299.03

Multiple choice:

A

B

C

D

E

F

G

H

D)

For this problem, what would be considered the null hypothesis?

A) H0: µ = 299.03

B) H0: µ > 299.03

C) H0: x-bar = 300

D) H0: x-bar > 300

E) H0: µ = 300

F) H0: µ > 300

G) H0: x-bar = 299.03

H) H0: x-bar > 299.03


8 of 13 5/2/2014 12:27 PM

Multiple choice:

A

B

C

D

E

F

G

H

E) For this hypothesis test, the null and alternative hypothesis are:

H0: µ = 300

Ha: µ < 300

If we assume that the null is true, what is the mean of the sampling distribution for x-bar?

Algebra:

300

Hints:

If we assume that the null is true, we can assume that µ = 300. Recall, that x-bar ~ N(µ ,σ/√n)

Therefore, we assume that the mean of the sampling distribution for x-bar = 300

F) If we assume that the null is true, what is the standard deviation of the sampling distribution for x-bar?

Round answer to the nearest hundredth.

Algebra:

1.22

1.23

Hints:

Rembember, the standard deviation for the sampling distribution of x-bar is σ/√n.

σ=3, n=6

σ/√n = 1.22 (ROUNDED)

G) What is the p-value for this problem? Round answer to the nearest hundredth.

Link to z-table

Algebra:

.21

.22

22

21

Hints:

P-value is P(x-bar < 299.03)

x-bar ~ N(300, 1.22)

z=-.79

P(x-bar < 299.03) = 0.2177


9 of 13 5/2/2014 12:27 PM

The p-value us 0.22 (ROUNDED)

H) If the level of significance is 0.05, the most appropriate conclusion would be:

Multiple choice:

We calculated a p-value of 0.22, which is greater than the stated significance level of 0.05. Therefore,

we fail to reject the null hypothesis.

One must state the conclusion in the context of the problem.


we fail to reject the null hypothesis. The data fails to support the claim that the company is under-

filling the bottles.


we reject the null hypothesis. The data supports the claim that the company is under-filling the bottles.

If the p-value is greater than alpha, we fail to reject the null. We fail to support the claim of the

Alternative Hypothesis.


we fail to reject the null hypothesis. The data proves that that the bottles have 300 milliliters (mL) of

nutrients.

Failing to reject the null DOES NOT prove the null hypothesis.

11) Problem #PRAKKG7 "PRAKKG7 - 276982 - For problems that..."

For problems that pertain to proportions one can say:

© STATS4STEM.ORG

Multiple choice:

Always use z and z* for hypothesis test and confidence interval calculations.

Always use t and t* for hypothesis test and confidence interval calculations.

Always use z and z* for proportions.

Always use z for hypothesis test calculations and t* for confidence interval calculations.


Always use t for hypothesis test calculations and z* for confidence interval calculations.


12) Problem #PRAKFE9 "PRAKFE9 - 273078 - Which of the foll..."

Which of the following are resistant? Check all that apply.

© STATS4STEM.ORG


10 of 13 5/2/2014 12:27 PM

Check all that apply:

a.

b

c

d

e

f

13) Problem #PRAJT8D "PRAJT8D - Harry - Coffee - CI"

A) Harry Potter decides to use his fame to start a coffee business called Magical Coffee. His first brand of

coffee was called Magic Potion #9. But sales were slow, so he decided to brew up a new type of coffee.

He decided to call his new brand of coffee Siriously Black. However, he wasn't sure if his new coffee was

actually better than his old coffee. So, he decided to run a blind taste test by choosing 12 coffee drinkers to

try the two types of coffee and rate both coffees on a scale of 1-10. To randomize the experiment, half the

drinkers were asked to drink Magic Potion #9 first, followed by Siriously Black. The other half were asked

to drink Siriously Black first, followed by Magic Potion #9. Based on the data below, calculate a 90%

confidence interval to estimate the mean impovement in the Siriously Black coffee over the Magic Potion.

Which of the following formulas should be used to calculate the confidence interval?

A.

B.

C.


11 of 13 5/2/2014 12:27 PM

D.

E.

© STATS4STEM.ORG

Multiple choice:

A

B

C

D

E

B) Calculate the lower number of the interval. Round answer to the nearest hundredth.

Link to t-table.

Algebra:

-.34

Hints:

t* = 1.796

x-bardiff

= 0.25

sdiff

= 1.1382

n = 12

Margin of Error = 0.59

Answer = -0.34

C)

Calculate the upper number of the interval. Round answer to the nearest hundredth.

Algebra:

0.84

Hints:

t* = 1.796

x-bardiff

= 0.25

sdiff

= 1.1382

n = 12

Margin of Error = 0.59

Answer = 0.84


12 of 13 5/2/2014 12:27 PM

14) Problem #PRAJVGP "PRAJVGP - 255824 - The following den..."

The following density curves represent different chi-square density curves for various degrees of freedom (df).

True or False:

As the degrees of freedom increase for the chi-square distribution, one needs a greater and greater chi-square test statistic to

reject the null.

© STATS4STEM.ORG

Multiple choice:

True

False

As the degrees of freedom increase, the rejection region moves further and further to the right.


13 of 13 5/2/2014 12:27 PM

Documents

Problem Set AP REVIEW ASSIGNMENT #8 …statsanswers.weebly.com/uploads/5/0/8/9/50891699/assistments_8.pdf · Problem Set "AP REVIEW ASSIGNMENT #8" id:[PSABTP9] Select All 1) Problem