# 10. if an experiment is conducted with 5 conditions and 6 subjects in

10. If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe?

17. Define three way interaction.

28. (AT) The dataset ADHD Treatment has four scores per subject. a. Is the design between-subjects or within-subjects? b. Create an ANOVA summary table.

29. (AT) Using the Anger Expression Index from the Angry Moods study as the dependent variable, perform a 2×2 ANOVA with gender and sports participation as the two factors. Do athletes and non-athletes differ signiﬁcantly in how much anger they express? Do the genders differ signiﬁcantly in Anger Expression Index? Is the effect of sports participation signiﬁcantly different for the two genders?

Use the following information to answer the next three exercises. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.

 Northeast South West Central East 16.3 16.9 16.4 16.2 17.1 16.1 16.5 16.5 15.6 17.2 16.4 16.4 16.6 16.5 6.6 16.5 16.2 16.1 16.4 16.8 X= s2 =

H0:µ1 =µ2 =µ3 =µ4 =µ5 Hα: At least any two of the group means µ1,µ2, …,µ5 are not equal.

61. degrees of freedom – numerator: df(num) = _________

63. Fstatistic = ________

69. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that Table 13.24 shows the results of a study.

 CNN FOX LOCAL 45 15 72 12 43 37 18 68 56 38 50 60 23 31 51 35 22

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

71. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study.

 White Black Hispanic Asian 6 4 7 8 8 1 3 3 2 5 5 5 4 2 4 1 6 6 7

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05

76. Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat’s weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again and the net gain in grams is recorded.

 Linda’s Rats Tuan’s Rats Javier’s Rats 43.5 47.0 51.2 39.4 40.5 40.9 41.3 38.9 37.9 46.0 46.3 45.0 38.2 44.2 48.6

Determine whether or not the variance in weight gain is statistically the same among Javier’s and Linda’s rats. Test at a significance level of 10%.

81. Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? Suppose that the Table 13.34 shows the results of a study

 Saturday Sunday Saturday Sunday 75 44 62 137 18 58 0 82 150 61 124 39 94 19 50 127 62 99 31 141 73 60 118 73 89

80.  In the North American court system, a defendant is assumed innocent until proven guilty.  In an ideal world, we would expect that the truly innocent will always go free, whereas the truly guilty ones will always be convicted.  Now, let us tackle the following questions?

1. In the context of the Type I error and Type II error, can you relate a court trial scenario in terms of these two errors?
2. What would be your ideal situation if you are the defendant?
3. What would be your ideal situation if you are the prosecuting attorney?
4. Lastly, what do you think of the scenario of an ideal world where we expect that no innocent will be found guilty and all guilty will be convicted in the context of Type I error and Type II error?

85.  My younger brother had a run in earlier with Médecins Sans Frontières.  He narrowly escaped from an adverse verdict by the court……..  What he wants is that he be left alone to run his small café……

He asked my oldest brother if he can conduct a survey for him about justice in the Kangaroo Court.  Oooops, I mean the Canadian Court…….

An initial survey was performed right after Médecins Sans Frontières accused my brother of wrong doing.  Of 1852 customers, 53 were against the aggressive tactics of Médecins Sans Frontières.  After my brother was cleared by the court, a follow-up survey was performed.  Of 4699 customers, 1751 said they did not agree with the aggressive tactics of Médecins Sans Frontières.

At the 1% significance level, do the data suggest that a higher percentage of customers were against Médecins Sans Frontières after the court case?

1. True or False. Justify for full credit.

(a) If P(A) = 0.4, P(B) = 0.5, and A and B are independent, then P(A AND B) = 0.9.

(b) If the variance of a data set is 0, then all the observations in this data set must be zero.

(c) The mean is always equal to the median for a normal distribution.

(d) A 95% confidence interval is wider than a 90% 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.

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

(a) Among the Senators in the current Congress, 54% are Republicans. The value 54% is a

(i) statistic

(ii) parameter

(iii) cannot be determined

(b) 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

(c) In a career readiness research, 100 students were randomly selected from the psychology program, 150 students were randomly selected from the communications program, and 120 students were randomly selected from cyber security program. This type of sampling is called:

(i) cluster

(ii) convenience

(iii) systematic

(iv) stratified

3. Choose the best answer. Justify for full credit.

(a) A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs

had 50 subjects in it. The subjects were followed for 12 months. Weight change for each

subject was recorded. You want to test the claim that the mean weight loss is the same for the

10 programs. What statistical approach should be used?

(i) t-test

(ii) linear regression

(iii) ANOVA

(iv) confidence interval

(b) A STAT 200 instructor teaches two classes. She wants to test if the variances of the score

distribution for the two classes are different. What type of hypothesis test should she use?

(i) t-test for two independent samples

(ii) t-test for matched samples

(iii) z-test for two samples

(iv) F- test

4. The frequency distribution below shows the distribution for IQ scores for a random sample of

1000 adults. (Show all work. Just the answer, without supporting work, will receive no credit.)

(a) Complete the frequency table with frequency and relative frequency. Express the relative

frequency to three decimal places.

(b) What percentage of the adults in this sample has an IQ score of at least 110?

(c) Does this distribution have positive skew or negative skew? Why or why not?

5. The five-number summary below shows the grade distribution of two STAT 200 quizzes for a

sample of 500 students.

For each question, give your answer as one of the following: (i) Quiz 1; (ii) Quiz 2; (iii) Both quizzes

have the same value requested; (iv) It is impossible to tell using only the given information. Then

(a) Which quiz has less range in grade distribution?

(b) Which quiz has the greater percentage of students with grades 85 and over?

(c) Which quiz has a greater percentage of students with grades less than 60?

6. A sample of 10 LED light bulbs consists of 1 defective and 9 good light bulbs. A quality

control technician wants to randomly select two of the light bulbs for inspection. Find the

probability that the first selected light bulb is good and the second light bulb is also good.

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

(a) Assuming the two random selections are made with replacement.

(b) Assuming the two random selections are made without replacement.

7. There are 1000 students in a high school. Among the 1000 students, 250 students take AP

Statistics, and 300 students take AP French. 100 students take both AP courses. Let S be the

event that a randomly selected student takes AP Statistics, and F be the event that a randomly

selected student takes AP French. 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 F).

(b) What is the probability of complement event of (S OR F)?

8. Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be

the event that the first one is a multiple of 3.

(a) What is the probability that the sum of the two dice is 8 given that the first one is a multiple of

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

(b) Are event A and event B independent? Explain.

9. Answer the following two questions. (Show all work. Just the answer, without supporting

work, will receive no credit).

(a) UMUC Stat Club is sending a delegate of 2 members to attend the 2016 Joint Statistical

Meeting in Chicago. There are 10 qualified candidates. How many different ways can the

delegate be selected?

(b) A bike courier needs to make deliveries at 6 different locations. How many different routes can

he take?

10. Assume random variable x follows a probability distribution shown in the table below.

Determine the mean and standard deviation of x. Show all work. Just the answer, without

supporting work, will receive no credit.

11. Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 cucumbers in her garden

which will be ready to harvest in about 10 days. Based on her experience, the probability of a

cucumber being eaten by the rabbits before harvest is 0.30.

(a) Let X be the number of cucumbers that Mimi harvests (that is, the number of cucumbers not

eaten by rabbits). 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 harvests at least 8 of the 10 cucumbers. (round the answer to 3

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

12. Assume the weights of men are normally distributed with a mean of 170 lbs and a standard

deviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive no

credit.

(a) Find the 75th percentile for the distribution of men’s weights.

(b) What is the probability that a randomly selected man weighs more than 200 lbs?

13. 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

(a) If a random sample of 64 test scores is selected, what is the standard deviation of the sample

mean?

(b) What is the probability that 64 randomly selected test scores will have a mean test score that is

between 475 and 525?

14. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a

90% confidence interval estimate of the proportion of adults believing in global warming. Show

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

15. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were

treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The

changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14.

Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the

garlic tablet treatment. Show all work. Just the answer, without supporting work, will receive

no credit.

16. Mimi is interested in testing the claim that banana is the favorite fruit for more than 80% of the

adults. She conducted a survey on a random sample of 100 adults. 85 adults in the sample

chose banana as his / her favorite fruit.

Assume Mimi 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 banana is the favorite fruit for more than

80% of the adults? Explain.

17. In a study of freshman weight gain, the measured weights of 5 randomly selected college

students in September and April of their freshman year are shown in the following table.

Is there evidence to suggest that the mean weight of the freshmen in April is greater than the

mean weight in September?

Assume we want to use a 0.10 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.

STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL1 Page 7 of 7

(d) Is there sufficient evidence to support the claim that the mean weight of the freshmen in April

is greater than the mean weight in September? Justify your conclusion.

18. In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats per

minute, and a standard deviation of 11.3 beats per minute. Based on the sample results, the

researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats

per minutes. Use a 0.05 significance level to test the researcher’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 the researcher’s claim? Explain.

19. 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.

(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

20. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam

score. A random sample of 5 students produced the following data where x is the average quiz

score and y is the final exam score.

(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 90? Show all work and justify your answer

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