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Final Exam Review MATH3339, Study Guides, Projects, Research of Statistics

University of Houston (UH)Statistics
Prof. Guoquan Wang

Final exam review sheet for Math3339 minimester 2025

Typology: Study Guides, Projects, Research

2024/2025

Uploaded on 05/29/2025

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Math 3339
Review for Final Exam
1. (Assuming a set has all positive values) If the largest value of a data set is doubled,
which of the following is not true?
a. The mean increases.
b. The standard deviation increases.
c. The interquartile range increases.
d. The range increases.
2. A potato chip company calculated that there is a mean of 74.1 broken potato chips in
each production run with a standard deviation of 5.2. If the distribution is
approximately normal, find the probability that there will be fewer than 60 broken chips
in a run.
3. What does it mean if the correlation coefficient, r, is close to 1? is close to 0?
4. In the regression equation y = b0 + b1x, identify what b0 and b1 represent. Which of
these will best explain the relationship between x and y?
5. Be able to identify type I and type II errors from an example.
6. It is fourth down and a yard to go for a first down in an important football game. The
football coach must decide whether to go for the first down or punt the ball away. The
null hypothesis is that the team will not get the first down if they go for it. The coach
will make a Type I error by doing what?
a. Deciding not to go for the first down when his team will get the first down.
b. Deciding not to go for the first down when his team will not get the first down.
c. Deciding to go for the first down when his team will get the first down.
d. Deciding to go for the first down when his team will not get the first down.
e. None of the above.
7. The following table displays the results of a sample of 100 in which the subjects
indicated their favorite ice cream of three listed. The data are organized by favorite ice
cream and age group. What is the probability that a person chosen at random will be
over 40 if he or she favors chocolate?
Age
Chocolate
Vanilla
Strawberry
Over 40
15
8
7
20 – 40
20
11
15
Under 20
8
7
9
pf3
pf4
pf5
pf8

Partial preview of the text

Download Final Exam Review MATH3339 and more Study Guides, Projects, Research Statistics in PDF only on Docsity!

Math 3339

Review for Final Exam

  1. (Assuming a set has all positive values) If the largest value of a data set is doubled, which of the following is not true? a. The mean increases. b. The standard deviation increases. c. The interquartile range increases. d. The range increases.
  2. A potato chip company calculated that there is a mean of 74.1 broken potato chips in each production run with a standard deviation of 5.2. If the distribution is approximately normal, find the probability that there will be fewer than 60 broken chips in a run.
  3. What does it mean if the correlation coefficient, r, is close to 1? is close to 0?
  4. In the regression equation y = b 0 + b1 x, identify what b 0 and b 1 represent. Which of these will best explain the relationship between x and y?
  5. Be able to identify type I and type II errors from an example.
  6. It is fourth down and a yard to go for a first down in an important football game. The football coach must decide whether to go for the first down or punt the ball away. The null hypothesis is that the team will not get the first down if they go for it. The coach will make a Type I error by doing what? a. Deciding not to go for the first down when his team will get the first down. b. Deciding not to go for the first down when his team will not get the first down. c. Deciding to go for the first down when his team will get the first down. d. Deciding to go for the first down when his team will not get the first down. e. None of the above.
  7. The following table displays the results of a sample of 100 in which the subjects indicated their favorite ice cream of three listed. The data are organized by favorite ice cream and age group. What is the probability that a person chosen at random will be over 40 if he or she favors chocolate?

Age Chocolate Vanilla Strawberry

Over 40 15 8 7

20 – 40 20 11 15

Under 20 8 7 9

  1. A random variable X has a probability distribution as follows:

X

P( X)

4k

5k

8k

3k

Find the probability that P( X < 2.0)

  1. The amount of time it takes a bat to eat a frog was recorded for each bat in a random sample of 12 bats. The resulting sample mean and standard deviation were 21.9 minutes and 7.7 minutes, respectively. Assuming it is reasonable to believe that the population distribution of bat mealtimes of frogs is approximately normal, a. Construct a 95% confidence interval for the mean time for a bat to eat a frog. b. Construct a 95% confidence interval for the variance of the time for a bat to eat a frog.
  2. Suppose that the average weekly grocery bill for a family of four is $140 with a standard deviation of $10. If the next 52 weeks can be viewed as a random sample from a population with this center and spread, then the approximate probability that the total grocery bill for one year is less than $7020 is 0.0002. This problem can also be solved using the sampling distribution of the sample average. Complete probability statement.
  3. One of your peers claims that boys do better in math classes than girls. Together you run two independent simple random samples and calculate the given summary statistics of the boys and the girls for comparable math classes. In Calculus, 15 boys had a mean percentage of 82.3 with standard deviation of 5.6 while 12 girls had a mean percentage of 81.2 with standard deviation of 6.7. Which of the following would be the most appropriate test for establishing whether boys do better in math classes than girls? a. two-sample z-test for means b. two-sample t-test for means c. chi-square test d. two-sample z-test for proportions e. none of these tests would be appropriate
  4. Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10 respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH units to all of the values and then multiply the result by 1.2. Find the mean and standard deviation of the corrected pH measurements.
  5. What is the expected value and the variance of the discrete probability function given in the table below?

Outcome 1 2 3 4 5 6 Probability .1 .2 .3 .3 0.

  1. The following data are for intelligence-test (IT) scores, grade-point averages (GPA), and reading rates (RR) of 20 at-risk students.

a. Calculate the line of best fit that predicts the GPA on the basis of IT scores. b. Calculate the line of best fit that predicts the GPA on the basis of RR scores. c. Which of the two lines calculated in parts a and b best fits the data?

  1. A manufacturer claims that its quality control is so effective that no more than 2% of the parts in each shipment are defective. A simple random sample of 100 parts from the last shipment contained 3 defectives. a. Why is a hypothesis test to determine the validity of the company’s claim inappropriate? Explain your answer. b. What is the smallest sample size for which a test of the claim would be appropriate at a significance level of 0.05? Show your work. c. Suppose your answer in part b were the sample size used. Perform an appropriate test of the manufacturer’s claim at the 5% level. Assume that the observed proportion is .03 for this sample size.
  2. A researcher claims that 90% of people trust DNA testing. In a survey of 100 people, 91 of them said that they trusted DNA testing. Test the researcher’s claim at the 1% level of significance.
  3. The dean of students of a large community college claims that the average distance that commuting students travel to the campus is 32 miles. The commuting students feel otherwise. A sample of 64 students was randomly selected and yielded a mean of 35 miles and a standard deviation of 5 miles. Test the dean’s claim at the 5% level.

IT 295 152 214 171 131 178 225 141 116 173

GPA 2.4 .6 .2 0 1 .6 1 .4 0 2.

RR 41 18 45 29 28 38 25 26 22 37

IT 230 195 174 177 210 236 198 217 143 186

GPA 2.6 0 1.8 0 .4 1.8 .8 1 .2 2.

RR^39 38 24 32 26 29 34 38 40

  1. A random sample of size 36 selected from a normal distribution with^ σ^ = 4 has x^ = 75. A second random sample of size 25 selected from a different normal distribution with σ (^) = 6 has x (^) = 85. Is there a significant difference between the two population means at the 5% level of significance?
  2. Find the z-score that corresponds to the given area under the standard normal curve.
  3. For the standard normal curve, find the z-score that corresponds to the 30th percentile.
  4. In an opinion poll, 25% of 200 people sampled said they were strongly opposed to the state lottery. The standard error of the sample proportion is approximately what?
  5. What is the critical value t* which satisfies the condition that the t distribution with 8 degrees of freedom has probability 0.10 to the right of t*?
  6. The one-sample t statistic for a test of based on n = 10 observations

has the value t = -2.25. What is the p-value for this test?

  1. Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 95% confidence interval of width of at most 0.05 for the probability of flipping a head?
  2. The guidance office of a school wants to test the claim of an SAT test preparation company that students who complete their course will improve their SAT Math score. Ten members of the junior class who have had no SAT preparation but have taken the SAT once were selected at random and agreed to participate in the study. All took the course and re-took the SAT at the next opportunity. The results of the testing indicated the values below. Is there significant evidence to support the claim that there is an improvement in the SAT scores after the test prep course?

Student 1 2 3 4 5 6 7 8 9 10 Before 475 512 492 465 523 560 610 477 501 420 After 500 540 512 530 533 603 691 512 489 458

Part of the resulting ANOVA table is

Source SS DF MS Treatments 38.820 3 12. Error 21.292 16 1.

a. Complete the ANOVA table. b. Perform a significance test to see if at least two of the are different. Use Tukey’s method to determine which pairs differ significantly.

  1. A study was conducted to determine whether remediation in basic mathematics enabled students to be more successful in an elementary statistics course. (Success here means C or better.) Here are the results of the study:

Remedial Non-remedial

Sample size 100 40

of successes 70 16

Test, at the 5% level, whether the remediation helped the students to be more successful.

  1. A preacher would like to establish that of people who pray, less than 80% pray for world peace. In a random sample of 110 persons who pray, 77 of them said that when they pray, they pray for world peace. Test at the 10% level.
  2. The data in the accompanying table resulted from an experiment run in a completely randomized design in which each of four treatments was replicated five times. Total Mean

Group 1 6.9 5.4 5.8 4.6 4.0 26.70 5. Group 2 8.3 6.8 7.8 9.2 6.5 38.60 7. Group 3 8.0 10.5 8.1 6.9 9.3 42.80 8. Group 4 5.8 3.8 6.1 5.6 6.2 27.50 5.

All Groups 135.60 6.

  1. Two methods were used to teach a high school algebra course. A sample of 75 scores was selected for method 1, and a sample of 60 scores was selected for method 2. The results are:

Method 1 Method 2

Sample mean 85 83

Sample s.d. 3 2

Test whether method 1 was more successful than method 2 at the 1% level.

  1. The table below displays the performance of 10 randomly selected students on the SAT Verbal and SAT Math tests taken last year.

Student 1 2 3 4 5 6 7 8 9 10

Math 475 512 492 465 523 560 610 477 501 420

Verbal 500 540 512 530 533 603 691 512 489 458

a. Calculate the least-squares regression line for this data. Report r and r-squared. b. Compute the 90% confidence interval. Interpret this confidence interval by describing for me in words what it means in the context of this problem. c. Is there a significant linear relationship between the variables? State the hypotheses, t-statistic, p-value, and conclusion.

  1. A midterm exam in Applied Mathematics consists of problems in 8 topical areas. One of the teachers believes that the most important of these is the section on problem solving. She analyzes the scores of 36 randomly chosen students using computer software and produces the following print-out relating the total score to the problem- solving subscore, ProbSolv:

Predictor Coef StDev T p s = 11. Constant 12.960 6.228 2.08 0.045 R-sq = 62.0% ProbSolv 4.0162 0.5393 7.45 0.000 R-sq (adj) = 60.9%

a. What is the regression equation? b. Interpret the slope of the regression in the context of the problem. c. Interpret the value of R-Sq in words. d. Calculate the 95% confidence interval of the slope of the regression line for all students. e. Use the information provided to test whether there is a significant relationship between the problem solving subsection and the total score at the 5% level.