Ask Question, Ask an Expert

+61-413 786 465

info@mywordsolution.com

Ask Statistics and Probability Expert

Question 1. True or False. Justify for full credit.

(a) If A and B are disjoint, P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2.

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

(c) There may be more than one mode in a data set.

(d) A 95% confidence interval is wider than a 98% confidence interval of the same parameter.

(e) In a two-tailed test, the value of the test statistic is 2. The test statistic follows a distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

1947_figure.png

Question 2. Choose the best answer. Justify for full credit.

(a) The quality control department of a semiconductor manufacturing company tests every 100th product from the assembly line. This type of sampling is called:

(i) cluster
(ii) convenience
(iii) systematic
(iv) stratified

(b) A study was conducted at a local college to analyze the trend of average GPA of all students graduated from the college. According to the Registrar, the average GPA for students with economics major from the class of 2016 is 3.5. The value 3.5 is a

(i) statistic
(ii) parameter
(iii) cannot be determined

(c) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is

(i) interval
(ii) nominal
(iii) ordinal
(iv) ratio

(d) 600 students took a chemistry test. You sampled 100 students to estimate the average score and the standard deviation. How many degrees of freedom were there in the estimation of the standard deviation?

(i) 599
(ii) 600
(iii) 99
(iv) 100

(e) You choose an alpha level of 0.05 and then analyze your data. What is the probability that you will make a Type I error given that the null hypothesis is true?

(i) 0.01
(ii) 0.025
(iii) 0.05
(iv) 0.10

Question 3. A random sample of 200 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours). (Show all work. Just the answer, without supporting work, will receive no credit.)

Study Time (in hours)

Frequency

Relative Frequency

0.0 - 5.0

6

 

5.1 - 10.0

24

 

10.1 - 15.0

50

 

15.1 - 20.0

 

0.35

20.1 - 25.0

 

 

Total

200

 

(a) Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places.
(b) What percentage of the study times was at most 15 hours?
(c) In what class interval must the median lie? 5.1 - 10.0, 10.1 -15.0, 15.1 - 20.0, or 20.1 - 25.0?
Why?

Question 4. The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 500 students.

1311_figure1.png

Answer each question based on the given information, and explain your answer in each case.

(a) What is the minimum in the grade distribution?
(b) Which quarter has the smallest spread of data? What is that spread?
(c) Find the interquartile range (IQR) in the grade distribution.
(d) Are there more students in the score band of 20 - 40 or 60 - 80? Why?
(e) Can the average score be determined based on the given information? Why or why not?

Question 5. A basket contains 2 white balls, 5 yellow balls, and 3 red balls. Consider selecting one ball at a time from the basket. (Show all work. Just the answer, without supporting work, will receive no credit.)

(a) Assuming the ball selection is with replacement. What is the probability that the first ball is red and the second ball is yellow?
(b) Assuming the ball selection is without replacement. What is the probability that the first ball is red and the second ball is also red?

Question 6. There are 1500 juniors in a college. Among the 1500 juniors, 600 students are taking STAT200, and 800 students are taking PSYC300. There are 500 students taking both courses. Let S be the event that a randomly selected student takes STAT200, and P be the event that a randomly selected student takes PSYC300. (Show all work. Just the answer, without supporting work, will receive no credit.)

(a) Provide a written description of the complement event of (S OR P).
(b) What is the probability of complement event of (S OR P)?

Question 7. Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at most 4, and B be the event that the first one is an odd number.

(a) What is the probability that the sum of the two rolls is at most 4 given that the first one is an odd number? Show all work. Just the answer, without supporting work, will receive no credit.
(b) Are event A and event B independent? Explain.

Question 8. Answer the following two questions. (Show all work. Just the answer, without supporting work, will receive no credit).

(a) Mimi has seven books from the Statistics is Fun series. She plans on bringing three of the seven books with her in a road trip. How many different ways can the three books be selected?
(b) A combination lock uses three distinctive numbers between 0 and 49 inclusive. How many different ways can the sequence of three numbers be selected?

Question 9. Imagine you are in a game show. There are 30 prizes hidden on a game board with 100 spaces. One prize is worth $100, nine are worth $50, and another twenty are worth $10. You have to pay $10 to the host if your choice is not correct. Let the random variable x be the money you get or lose. Show all work. Just the answer, without supporting work, will receive no credit.

(a) Complete the following probability distribution.

x

P(x)

-$10

 

$10

 

$50

 

$100

 

(b) What is your expected winning or loss in this game? Be specific in your answer whether it's winning or loss.

Question 10. Mimi joined UMUC basketball team in spring 2017. On average, she is able to score 30% of the field goals. Assume she tries 15 field goals in a game.

(a) Let X be the number of field goals that Mimi scores in the game. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?
(b) Find the probability that Mimi scores at least 3 of the 15 field goals. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.

Question 11. A research concludes that the number of hours of exercise per week for adults is normally distributed with a mean of 4 hours and a standard deviation of 3 hours. Show all work. Just the answer, without supporting work, will receive no credit.

(a) What is the probability that a randomly selected adult has more than 7 hours of exercise per week (round the answer to 4 decimal places)
(b) Find the 80th percentile for the distribution of exercise time per week. (round the answer to 2 decimal places)

Question 12. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no credit.

(a) Consider all random samples of 64 test scores. What is the standard deviation of the sample means? (Round your answer to three decimal places)
(b) What is the probability that 64 randomly selected test scores will have a mean test score that is greater than 525? (Round your answer to four decimal places)

Question 13. A city built a new parking garage in a business district. For a random sample of 100 days, daily fees collected averaged $2,500, with a standard deviation of $500. Construct a 90% confidence interval estimate of the mean daily income this parking garage generates. Show all work. Just the answer, without supporting work, will receive no credit.

Question 14. Mimi conducted a survey on a random sample of 100 adults. 70 adults in the sample chose banana as his / her favorite fruit. Construct a 95% confidence interval estimate of the proportion of adults whose favorite fruit is banana. Show all work. Just the answer, without supporting work, will receive no credit.

Question 15. A researcher is interested in testing the claim that more than 75% of the adults believe in global warming. She conducted a survey on a random sample of 400 adults. The survey showed that 320 adults in the sample believe in global warming.
Assume the researcher wants to use a 0.05 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that more than 75% of adults believe in global warming? Explain

Question 16. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table.

 

Number of Words Recalled

Subject

1 hour later

24 hours later

1

2

3

4

5

13
18

10

15

11

12

16

9

13

11


Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Assume we want to use a 0.05 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion.

Question 17. John oversees a bottle-filling machine in a company. The amount of fluid dispensed into each bottle is approximately normally distributed with an unknown population standard deviation. On a particular day, a random sample of 50 bottles yielded a mean of 357.2 ml and a standard deviation of 15.8 ml. John then concluded that the population standard deviation of the fluid dispense amount by the machine is greater than 15 ml.
The lead engineer wants to use a 0.01 significance level to test John's claim.

(a) Identify the null hypothesis and alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support John's claim that the population standard deviation of the fluid dispense amount by the machine is greater than 15 ml? Explain.

Question 18. The UMUC Daily News reported that the color distribution for plain M&M's was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M's was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer.

Color

Brown

Yellow

Orange

Green

Tan

Number

42

21

12

7

18

(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value. Show all work; writing the correct P- value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer.

Question 19. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score. A random sample of 10 students produced the following data where x is the average quiz score and y is the final exam score.

x

72

94

55

63

100

40

85

70

75

85

y

70

96

50

70

96

50

83

75

77

87

(a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.
(b) Based on the equation from part (a), what is the predicted final exam score if the average quiz score is 80? Show all work and justify your answer.

Question 20. A study of 15 different weight loss programs involved 300 subjects. Each of the 15 programs had 20 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. We want to test the claim that the mean weight loss is the same for the 15 programs.

(a) Complete the following ANOVA table with sum of squares, degrees of freedom, and mean square (Show all work):

Source of Variation

Sum of Squares
(SS)

Degrees of Freedom
(4f)

Mean Square
(318)

Factor
(Between)

42.5

 

 

Error
(Within)

 

 

 

Total

553.05

299

N/A

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the mean weight loss is the same for the 15 programs at the significance level of 0.10? Explain.

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M92483753
  • Price:- $70

Priced at Now at $70, Verified Solution

Have any Question?


Related Questions in Statistics and Probability

An athletics coach states that the distribution of player

An athletics coach states that the distribution of player run times (in seconds) for a 100-meter dash are normally distributed with a mean equal to 14.00 and a standard deviation equal to 0.2 seconds. What percentage of ...

How would i calculate this the personnel office at a large

How would I calculate this :The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first i ...

An independent-measures study has one sample with n 10 and

An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments. What is the df value for the t statistic for this study?

A business analyst in the washington dc area looked at the

A business analyst in the Washington, D.C. area looked at the following Christmas 2016 and 2017 toy sales in Metro D.C. Six toy stores were were contacted and shared the following information where x is 2016 sales and y ...

According to the deloitte ev survey 5 of respondents

According to the Deloitte EV Survey, 5% of respondents indicated that they would be willing to pay an extra $500 or more for an electric vehicle versus one with a gasoline engine. A random sample of 25 adults has been se ...

The meantime it takes a technician to resolve this software

The meantime it takes a technician to resolve this software issue is 18 minutes with a standard deviation of 4.2 minutes. This information was obtained from a random sample of 10 monitored calls. A sample of 15 monitored ...

New york graduates tend to leave the state after graduating

New York graduates tend to leave the state after graduating. A study asked the students of NYU "Are you planning to stay in NY after graduation?" In the sample, only 37% answered yes. The study explained that with a 95% ...

Use the information below to answer the questions that

Use the information below to answer the questions that follow : While the Mars candy company no longer reports the percentages of each color M&M that are produced, they had previously reported the following: 13% brown  1 ...

A test of the null A test of the null hypothesis  H 0 :  μ  =  μ 0  gives test statistic 

A test of the null hypothesis  H 0 :  μ  =  μ 0  gives test statistic  z  = -0.58  (Round your answers to four decimal places.) a) What is the  P -value if the alternative is  H a :  μ  >  μ 0 ? b) What is the  P -value ...

In a panel discussion with 3 industry reps 2 government

In a panel discussion with 3 industry reps, 2 government reps, and 1 association rep, how many ways can they be seated along a row a) With no restrictions (each person can sit anywhere)? b) If the 3 industry reps must si ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

Compute the present value of an 1150 payment made in ten

Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As