STAT200 Final Exam Summer 2021

1. Decide if following statements are True or False.

(a) If the variance of a data set is 0, then all the observations in this data set must be zero. (b) The volume of milk in a jug of milk is a discrete data. (c) Median is equal mean only if the distribution is symmetrical. (d) Last Name is a nominal type of variable.

2. The vine producer should send 80 bottles of vine to supermarket. Before he ships the boxes he decided to check 5 different bottles. Describe how he should select these 5 bottles using systematic selection.

3. The table below shows the frequency distribution of IQ scores for a random sample of 1000 adults.

IQ Scores Frequency Cumulative Relative

Frequency

50 – 69 23

70 – 89 249

90 -109 0.743

110 – 129

130 – 149 25

Total 1000

Complete the table with missing frequency and cumulative frequency.

4. The Box-Plot below shows the grade distribution of a quiz for a sample of 160 students. Answer each question based on the given information and explain your answer in each case.

(a) Which interval has the fewest students?

• 30 – 50 • 50 – 70 • 70 – 90 • cannot be determined

(b) How many students in the sample are in the score band between 50 and 70?

5. Consider selecting one card at a time from a 52-card deck. What is the probability that the first card is a Queen, and the second card is also a Queen? (Note: There are 4 Queens in a standard deck of cards) (Show all work. Just the answer, without supporting work, will receive no credit.)

(a) Assuming the card selection is with replacement. (b) Assuming the card selection is without replacement.

6. There are 500 juniors in a college. Among the 500 juniors, 200 students are taking STAT200, and 120 students are taking PSYC300. There are 50 students taking both courses. (200+120 is less than 500 because some students do not take STAT or PSY). What is the probability that randomly selected junior in this college takes STAT200 or PSY300? (Show work. Just the answer, without supporting work, will receive no credit.)

7. Consider rolling a fair 6-faced die twice. What is the probability that the sum of the two rolls will be 7?

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

8. (a) Probability 5/16 convert to Odds (b) Odds 3 to 5 convert to probability.

9. (a) Jenny has six textbooks from her college courses. She plans on bringing three of these textbooks with her in a road trip. In how many ways can she select these three books?

(b) Board of Directors must appoint a president, a vice president, and a treasurer. There are 5 qualified candidates. In how many ways can the officers be appointed?

10. For the given below Discrete Distribution, calculate Expected Value (Mean).

2 5 6 9 12

0.1 0.2 0.4 0.2 0.1

11. For the Binomial Distribution with n = 15 trials and probability of success in each trial p = 0.68 find probability of s = 10 successes.

Use online Binomial calculator: https://www.thecalculator.co/math/Binomial-Calculator-741.html

12. A basketball player has p = 0.74 probability to succeed in Free Throw. If he will make 15 Free Throws find the probability that 10 or more will be successful?

Use online Binomial Calculator: https://www.thecalculator.co/math/Binomial-Calculator-741.html

13. For Normal Distribution with a mean μ=20 and a standard deviation σ= 4 find the probability

(a) that x is greater than 25 (b) that x is between 18 and 22 . Use online Normal Distribution Calculator: https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php

14. The GRE scores has Normal Distribution with a population mean μ =160 and a standard deviation σ = 24. What is the probability the mean of 36 randomly selected test scores will have a mean test score between 155 and 165? (Tip. This will be a distribution of sample mean. Change σ from 24 to 24/√36).

15. A survey shows that 650 of the 1000 adult respondents believe in human activity driven global warming. Construct a 95% confidence interval estimate of the proportion of adults believing in global warming. Show work. Just the answer, without supporting work, will receive no credit.

16. A researcher claims the proportion of auto accidents that involve teenage drivers is less than 20%. ABC Insurance Company checks police records on 200 randomly selected auto accidents and notes that teenagers were at the wheel in 32 of them. Use a 0.05 significance level to test the researcher’s claim.

• Identify the null hypothesis and the alternative hypothesis. • Determine z-value for the test statistic • Use website https://www.socscistatistics.com/pvalues/normaldistribution.aspx

and determine the P-value for this test. • Is there sufficient evidence to support the researcher’s claim that the proportion of auto accidents that

involve teenage drivers is less than 20%? Explain.

Show work; writing the correct answer, without supporting work, will receive no credit.

17. Perform a Hypothesis Test if regular excise really helps weight loss. Table below shows results for 5 people doing 30- minute exercise every day for 6 months. Does the data below suggest that the regular exercise helps weight loss? Apply significance level 0.05

Weight (pounds)

Subject Before After

1 250 240

2 240 235

3 215 210

4 220 200

5 200 190

• Identify the null hypothesis Ho and the alternative hypothesis HA. • Create column for d-column for differences between weight before and weight after. • Calculate mean (�̅� ) and standard deviation (s) for numbers in difference column.

• Determine the test statistic t = �̅� − 0 𝑠

√𝑛⁄

• Use website https://www.socscistatistics.com/pvalues/tdistribution.aspx to find p-value. • Should we reject or do not reject Ho.

18. 300 randomly selected people asked how they prefer to spend a vacation.

results are in the table. Use a 0.05 significance level to test the claim that preferences are evenly distributed.

Stay At Home

On the Beach

Caribbea n Cruise

Travel in US

Travel Abroad

56 59 68 65 52

• This is Chi-Square Test of Uniform. Identify Ho and HA. • Given numbers represent Observed values (O). Expected values for Uniform distribution should

be the same for all 5 categories. To find Expected value (E) divide total number of answers by 5.

Create a table with O- and E-columns.

• Calculate (O-E)2/E for each category and find Chi-Square. • Use website https://www.socscistatistics.com/pvalues/chidistribution.aspx and find p-value. • Is there sufficient evidence to support Ho?

Show work; without supporting work, you will receive no credit.

19. Based on coordinates x and y given in the table, find the equation of regression line.

X 10 20 30 40 50 60 70 80 y 35 48 52 60 64 74 76 84

20. A study of 8 different weight loss programs involved 160 subjects. Each of the 8 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 8 programs.

Source of Variation

Sum of Squares

(SS) Degrees of Freedom

(df)

Mean Square

(MS)

Factor (Between) 32

Error (Within)

Total 300 159 ———-

• Complete the following ANOVA table ( explain how you get your numbers): • Determine the F-value as F = (MS)between/(MS)within • Apply online applet https://www.danielsoper.com/statcalc/calculator.aspx?id=105 and find p-value. • Is there sufficient evidence to support the Ho that the mean weight loss is the same for all 8 group?

End of the Final Exam

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