Stat200 week8 complete solutions correct answers key

Stat200 week8 complete solutions correct answers key

I.                      Question 1 (15 points)

Question 1 options:

Question 1 (5 pts.)

True or False.

Enter the answer to each of the of the questions with:

  T for True     F for False

a.      If all the observations in a data set are identical, then the variance for this data set is zero.

b.         If:

P(A) = 0.4

P(B) = 0.5

A and B are disjoint

then

P(A AND B) = 0.2.

c.      Assume X follows a distribution which is symmetrical about 0.

  If P(X>2) = 0.3  then  P(X< -3) most be less than 0.3.

d.      A 95% confidence interval is wider than a 90% confidence interval of the same parameter.

e.      In a right-tailed hypothesis, the test statistic is 1.5.  If we know P(X<1.5) = 0,96, then we reject the null hypothesis at .05 level of significance.

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II.                   Question 2 (5 points)

Question 2 options:

Question 2 (5 pts.)

Refer to the following frequency distribution for Questions 2, 3, 4, and 5.

Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours).

Checkout Time (in minutes)

Frequency

Relative Frequency

  1.0 - 1.9

3

C

  2.0 - 2.9

12

D

  3.0 - 3.9

A

0.20

  4.0 - 4.9

3

E

  5.0 - 5.9

B

F

Total

25

G

Complete the Frequency Table with the missing frequency and relative frequency numbers.

Enter answer for "A" as a integer.

Enter answer for "B" as an integer.

Enter answer for "C" as a 2 decimal place number with a zero to the left of the decimal point.

Enter answer for "D" as a 2 decimal place number with a zero to the left of the decimal point.

Enter answer for "E" as a 2 decimal place number with a zero to the left of the decimal point.

Enter answer for "F" as a 2 decimal place number with a zero to the left of the decimal point.

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III.                Question 3 (3 points)

Question 3 options:

Question 3 (3 pts.)

A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours).

This is the same distribution table from Question 2

Checkout Time (in minutes)

Frequency

Relative Frequency

  0.0 - 4.9

5

    A

  5.0 - 9.9

13

    B

  10.0 - 14.9

C

    0.22

  15.0 - 19.9

42

    D

  20.0 - 24.9

E

    F

Total

100

    G

What percentage of the study times was at least 15 hours?

Enter answer as a percent without the percent sign to 0 decimal places.

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IV.                Question 4 (5 points)

Question 4 options:

Question (4 pts.)

A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours).

This is the same distribution table from Question 2

Checkout Time (in minutes)

Frequency

Relative Frequency

  1.0 - 1.9

5

C

  2.0 - 2.9

12

D

  3.0 - 3.9

A

0.20

  4.0 - 4.9

3

E

  5.0 - 5.9

B

F

Total

25

G

In what class interval must the median lie? Explain your answer.
Enter answer by selecting the appropriate letter.

a     Interval 1    (1.0 - 1.9)

b     Interval 2    (2.0 - 2.9)

c     Interval 3    (3.0 - 3.9)

d     Interval 4    (4.0 - 4.9)

e     Interval 5    (5.0 - 59)

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V.                   Question 5 (2 points)

Question 5 options:

Question 5 (2 pts.)

A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours).

This is the same distribution table from Question 2.

Checkout Time (in minutes)

Frequency

Relative Frequency

  0.0 - 4.9

5

    A

  5.0 - 9.9

13

    B

  10.0 - 14.9

C

    0.22

  15.0 - 19.9

42

    D

  20.0 - 24.9

E

    F

Total

100

    G

The distribution is negatively skewed, symmetrical, positively skewed?

Answer question by entering appropriate letter.

a     negatively skewed

b     symmetrical

c     positively skewed

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VI.                Question 6 (5 points)

Question 6 options:

Question 6 (5 pts.)

Consider selecting one card at a time from a 52-card deck.  (Note: There are 4 aces in a deck of cards.)

If the card selection is without replacement, what is the probability that the first card is an ace and the second card is an ace?

Express the answer in simplest fractional form, or as a decimal rounded to 4 decimal places with a 0 to the left of the decimal point.

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VII.             Question 7 (5 points)

Question 7 options:

Question 7 (5 pts.)

Consider selecting one card at a time from a 52-card deck.  (Note: There are 4 aces in a deck of cards.)

If the card selection is with replacement, what is the probability that the first card is an ace and the second card is an ace?

Express the answer in simplest fractional form, or as a decimal rounded to 4 decimal places with a 0 to the left of the decimal point.

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VIII.          Question 8 (4 points)

Question 8 options:

Quiz 8 (4 pts.)

The 5-number summary below shows the grade distribution of two Stat 200 quizzes.

Minimum

Q1

Median

Q3

Maximum

Quiz 1

15

45

55

85

100

Quiz 2

20

35

50

90

100

Which quiz has less interquartile range in grade distribution?

a   Quiz 1

b   Quiz 2

c   Both quizzes have the same value requested.

d   It is impossible to tell using the given information.

Answer the question by keying in the appropriate letter.                                                              

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IX.                Question 9 (4 points)

Question 9 options:

Question 9 (4 pts.)

The 5-number summary below shows the grade distribution of two Stat 200 quizzes.

Minimum

Q1

Median

Q3

Maximum

Quiz 1

15

45

55

85

100

Quiz 2

20

35

50

90

100

Which quiz has the greater percentage of students with grades of 90 or over?

a   Quiz 1

b   Quiz 2

c   Both quizzes have the same value requested.

d   It is impossible to tell using only the given information.

Answer the question by keying in the appropriate letter.                                                                           

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X.                   Question 10 (4 points)

Question 10 options:

Question 10 (4 pts.)

The 5-number summary below shows the grade distribution of two Stat 200 quizzes.

Minimum

Q1

Median

Q3

Maximum

Quiz 1

15

45

55

85

100

Quiz 2

20

35

50

90

100

Which quiz has lthe greatest number of students with grades less than 60?

a   Quiz 1

b   Quiz 2

c   Both quizzes have the same value requested.

d   It is impossible to tell using only the given information.

Answer the question by keying in the appropriate letter.                                                                           

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XI.                Question 11 (10 points)

Question 11 options:

Question 11 (10 pts.)

There are 1000 students in a high school.

Among the 1000 students

800 students have a laptop

300 students have a tablet

150 students have both devices

What is the probability that a randomly selected student has neither device?

Enter answer as a reduced fraction or a 2 place decimal with a 0 to the left of the decimal point.

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XII.             Question 12 (5 points)

Question 12 options:

Question 12 (5 pts.)

There are 1000 students in a high school.

Among the 1000 students

800 students have a laptop

300 students have a tablet

150 students have both devices

What is the probability that a randomly selected student has a laptop, given that he/she has a tablet?

Enter answer as a reduced fraction or a 2 place decimal with a 0 to the left of the decimal point.

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XIII.          Question 13 (5 points)

Question 13 options:

Question 13 (5 pts.)

There are 1000 students in a high school.

Among the 1000 students

800 students have a laptop

300 students have a tablet

150 students have both devices

Let event A be the selected student having a laptop, and event B be the selected student having a tablet.

Are A and B independent events?

If the events are Independent enter answer Y for Yes.

If the events are not independent enter N for No.

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XIV.          Question 14 (5 points)

Question 14 options:

Question 14 (5 pts.)

A combination lock uses three distinctive numbers between 0 and 49 inclusive.

How many different ways can a sequence of three be selected if numbers are allowed to repeat?

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XV.             Question 15 (15 points)

Question 15 options:

Question 15 (15 pts.)

Let random variable x represent the number of heads when a fair coin is tossed three times.

a.    Complete the table describing the probability distribution and answer the following questions.

Number of Heads (x)

Probability of x

0

A

1

B

2

C

3

D

Enter the  numerical values of A, B, C, D respectively as a reduced fraction or a 3 place decimal with a zero to the left of the decimal place.

b.    Determine the mean value of x.

Enter answer rounded to 2 decimal places.

c.    Determine the standard deviation of x.

Enter answer rounded to 2 decimal places.

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XVI.          Question 16 (14 points)

Question 16 options:

Question 16 (15 pts.)

Mimi just started her tennis class three weeks ago.

On average, she is able to return 20% of her opponent’s serves.

Assume her opponent serves 10 times.

Let X be the number of returns that Mimi gets.

As we know, the distribution of X is a binomial probability distribution.

What is the number of trials (n)?
Enter answer as an Integer.
 
What is the probability of a success (p)?

What is the probability of a failure (q)?

Answer the three questions from left to right respectively. 
Enter each answer to 1 decimal place with a 0 to the left of the decimal point.
Do not enter answer as a percent.

Find the probability that that she returns at least 1 of the 10 serves from her opponent.

Enter answer to 4 decimal places.
Do not enter answer as a percent.

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XVII.       Question 17 (5 points)

Question 17 options:

Question 17 (5 pts)

The lengths of mature jalapeno fruits are normally distributed with a mean of 3 inches and a standard deviation of 1.

What is the probability that a randomly selected mature jalapeno fruit is between 1.5 and 4 inches long?

Enter answer as a decimal rounded to 4 decimal places with a 0 to the left of the decimal point.

Do not enter answer as a percent.

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XVIII.    Question 18 (5 points)

Question 18 options:

Question 18 (5 pts.)

The lengths of mature jalapeno fruits are normally distributed with a mean of 3 inches and a standard deviation of 1.

Find the 90th percentile of the jalapeno fruit length distribution.

Enter answer as a decimal rounded to 2 decimal places.

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XIX.          Question 19 (5 points)

Question 19 options:

Question 19 (5 pts.)

The lengths of mature jalapeno fruits are normally distributed with a mean of 3 inches and a standard deviation of 1.

If a random sample of of 100 mature jalapeno fruits is selected, what is the standard deviation of the sample mean.

Enter answer as a reduced fraction or a decimal rounded to 1 decimal place with a 0 to the left of the decimal point.

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XX.             Question 20 (8 points)

Question 20 options:

Question 20 (8 pts.)

A random sample of 100 light bulbs has a mean lifetime of 3000 hours

Assume that the  population standard deviation of the light bulbs is 500 hours.

Construct a 95% confidence interval estimate of the mean lifetime.

Enter the lower and upper confidence limit numbers rounded to 0 decimal places (Integer) respectively.

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XXI.          Question 21 (15 points)

Question 21 options:

Question 21 (15 pts.)

Consider the hypothesis test given by                                   

Ho: p = 0.5

H1: p < 0.5

In a random sample of 100  subjects, the sample proportion is found to be phat = 0.45

What is the appropriate distribution for performing the hypothesis test?

a    Uniform distribution

b     z distribution

c     t distribution

d     Chi square distribution

e     F distribution

Enter appropriate letter for answering this question.

Determine the numerical value of the test statistic.

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

Determine the p-value for this test.

Enter answer rounded to 2 decimal places with a zero to the left of the decimal point.

Is there sufficient evidence to justify the rejection of Ho at an α = .01 level?

a     Yes: There is sufficient evidence to justify the rejection of Ho at an α = .01 level

b     No:  There is insufficient evidence to justify the rejection of Ho at an α = .01 level

Enter your answer by selecting the appropriate letter.

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XXII.       Question 22 (15 points)

Question 22 options:

Question 22 (15 pts.)

Consumption of a large amount of alcohol is known to increase reaction time.  To investigate the effects of small amounts of alcohol, reaction time was recorded for five individuals before and after 2 ounces of alcohol was consumed by each.

Does the data below suggest that the consumption of 2 ounces of alcohol increases the mean reaction time?

Assume we want to use a 0.01 significance level to test the claim.

Reaction Time (seconds)

Subjects

Before

After

1

6

7

2

8

8

3

4

6

4

7

8

5

9

8

Identify the null hypothesis and the alternative hypothesis.

a     Ho     There is no difference in reaction time with or without the alcohol consumption.
       Ha     There is a difference in reaction time with alcohol consumption.