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Review questions for Final Exam T / F 1. Height is an example of quantitative data. T / F 2. If data has a right (positively) skewed unimodal histogram, the median will be to the right of the mean. T / F 3. In a sample of size 25, the median is the average of the 12th and 13th largest values. T / F 4. If the null hypothesis is not rejected, then we have proved that the null hypothesis is true. T / F 5. The p-value is the probability, assuming 𝐻0 is true, of obtaining a value of the test statistic higher than or farther away from expected as what actually resulted. T / F 6. If you toss a “fair” coin 100 times, you will observe exactly 50 heads. T / F 7. 𝑥̅ , s and σ are sample statistics. T/F 𝜎 8. The margin of error 𝑧 ∗ ( 𝑛) of a confidence interval for 𝜇 decreases as n increases. √ T / F 9. µ represents the sample mean. T / F 10. In simple linear regression, if the null hypothesis is rejected in a test of 𝐻0 : 𝛽 = 0, there is a useful linear relationship between x and y , so that values of x may help predict y. T / F 11. In the simple linear regression model, 𝛽 ( the true slope of the regression line) can be interpreted as the amount y will be expected to change when the value of the predictor variable x is increased by one unit. T / F 12. When a scatterplot is used to graph a bivariate data set, the variable plotted on the y-axis is the response variable while the variable plotted on the x-axis is the predictor (explanatory) variable. T / F 13. In hypothesis testing, a small p-value indicates that the observed sample results are inconsistent with the null hypothesis. T / F 14. The null hypothesis should be rejected when the p-value is larger than the significance level of the test. T / F 15. Two outcomes are independent if the chance that one outcome occurs is unaffected by knowledge of whether or not the other occurred. T / F 16. The mean is the middle value of an ordered data set. T / F 17. The 68-95-99.7 Rule can only be used when the data are approximately normal. T / F 18. s is the sample standard deviation. T / F 19. A z-score tells how many standard deviations a value is from the mean. T / F 20. If the correlation coefficient r between x and y is 0, then there is no correlation seen between x and y. T / F 21. A value of Pearson’s correlation coefficient r that is close to 1 indicates that there is a strong relationship between two variables. 22. A manufacturer of cellular phones has decided that an assembly line is operating satisfactorily if less than 3% of the phones produced per day are defective. To check the quality of a day's production, the company decides to randomly sample 30 phones from a day's production to test for defects. Define the population of interest to the manufacturer. A. All the phones produced by the manufacturer. C. The 30 responses: defective or not defective. B. The 30 phones sampled and tested. D. The 3% of the phones that are defective. 23. A manufacturer of cellular phones has decided that an assembly line is operating satisfactorily if less than 3% of the phones produced per day are defective. To check the quality of a day's production, the company decides to randomly sample 30 phones from a day's production to test for defects. State the null and alternative hypotheses for a test. A. 𝐻0 : 𝜇 = 0.03 vs. 𝐻𝑎 : 𝜇 > 0.03 C. 𝐻0 : 𝑝 = 0.03 vs. 𝐻𝑎 : 𝑝 < 0.03 B. 𝐻0 : 𝑝 = 0.03 vs. 𝐻𝑎 : 𝑝 > 0.03 D. 𝐻0 : 𝜇 = 0.03 vs. 𝐻𝑎 : 𝜇 < 0.03 24. For a random variable z which has a standard normal distribution, P(z < 2.10) = a. 0.4821 b. 0.0179 c. 0.9821 d. none of these 25. Suppose the random variable X has a normal distribution with mean 9.0 and variance 49. The probability that X takes on a value of at least 18 is approximately equal to a. 0.0985 b. 0.4286 c. 0.9015 d. correct approx. answer not given 26. If the slope of the regression line is negative and the coefficient of determination (r-squared) is .64, then the correlation coefficient is a. 0.64 b. 0.8 c. -0.64 d. -0.8 27. The percentage of points falling below the 75th percentile is a. 25% b. 75% c. can’t say 28. In a two-tailed test with calculated test statistic z = 1.68, the p-value is a. .0930 b. .0465 c. .9170 d. .9535 29. The probability that a normal variable X falls within 2 standard deviations of the mean is a. .0228 b. .9772 c. .0456 d. .9544 For problems 30 through 35, consider the following data set which consists of measurements of the daily emission of sulfur oxides (in tons) for an industrial plant. { 15.8, 18.7, 6.2, 17.5, 11.0, 19.0, 26.4, 13.9, 14.7 } 30. What is n, the size of the sample? a. 9 b. 10 c. 8 d. 143.20 31. What is 𝑥̅ , the sample mean? a. 17.9 b. 15.91 c. 143.20 d. can’t say e. can’t say 32. 𝑥̅ , the sample mean, and s, the sample standard deviation, are examples of a. statistics b. parameters c. neither of these 33. What is µ , the population mean? a. 17.9 b. 15.91 c. 143.20 d. can’t say 34. Considering this sample of data provided, would you describe this data set as skewed? If so, why? If not, why not? 35. Find the 5-number summary and construct a boxplot for this sample. 36. Which of the following is a measure of the variability of a distribution? A. Skewness B. Median C. Standard deviation D. z-score 37. Which of the following will reduce bias in a study? I. A larger sample size. II. A controlled experiment. III. A random sample. A. I and II B. I and III C. II and III D. I, II & III E. None of these. 38. Are Women Getting Taller? A researcher claims that the average height of a woman aged 20 years or older is greater than the 1994 mean height of 63.7 inches, on the basis of data obtained from the Centers for Disease Control and Prevention’s, Advance Data Report, No. 347. She obtains a random sample of 45 women and finds the sample mean height to be 63.9 inches. Assume that the population standard deviation is 3.5 inches. Test the researcher’s claim at the 0.05 level of significance. 39. For each of the population parameters, write the symbol for the corresponding sample statistic, and the name of the statistic. Sample estimate symbol Sample estimate name σ ______ ________________________ µ _______ ________________________ p _______ ________________________ 40. Make a back-to-back stemplot to compare the data from the two groups below. Male scores: 14, 17, 22, 36, 36, 37, 41, 43 Female scores: 16, 17, 17, 20, 26, 30, 45, 46 41. The index of biotic integrity (IBI) is a measure of the water quality in streams. IBI and land use measures for a collection of streams in the Ozark Highland ecoregion of Arkansas were collected as part of a study. The following output investigates the relationship between IBI and the area of the watershed in square kilometers for streams with area less than or equal to 70 km2. SUMMARY OUTPUT Regression Statistics Multiple R 0.445923 R Square 0.198847 Adjusted R Square 0.181801 Standard Error 16.53465 Observations 49 Coefficients 52.92296 0.460155 Intercept Area Standard Lower Upper Error t Stat P-value 95% 95% 4.483524 11.80387 1.17E-15 43.90327 61.94264 0.134727 3.415471 0.001322 0.18912 0.73119 100 IBI 0 0 50 Area 100 Predicted IBI Area Residual Plot Residuals IBI Area Line Fit Plot 100 0 -100 0 20 40 Area Frequency Histogram of residuals 15 10 5 0 A. What is the correlation between watershed area and IBI? _________ B. What is the value of r-squared? __________ C. Write a sentence interpreting the coefficient of determination above. D. Examine the scatterplot, and describe the strength, direction and form of the relationship. 60 80 E. Give the equation of the regression line. ____________________________________________________ F. State hypotheses that are appropriate to address the question of whether there is a significant relationship between watershed area and IBI. G. What assumptions must be met to conduct a significance test to determine whether the relationship between watershed area and IBI? Are they met? Explain. H. State the test statistic value and report a p-value. I. State a conclusion, both in statistical terms, comparing the p-value, and in a sentence that someone who knows no statistics would understand. 42. A city has 10 low-income housing complexes, having the following numbers of apartments. 1 20 2 40 3 40 4 80 5 40 6 20 7 60 8 40 9 40 10 20 The city council wishes to start a program offering additional education to low-income residents, and wants to determine the current educational level in each apartment. They decide to sample 20 apartments. a. Explain how the council might randomly select 20 apartments in which to determine education levels. Be sure to carefully consider your sampling design. b. Using the random digits table line 105, choose the first 3 apartments that will be sampled based on your design above. Your numbers will depend on your design. Be sure to specify how you are numbering the apartments in your design. 43. An article reported that in a survey of 800 people, 42% said they prefer spaghetti to linguini. Find a 97% confidence interval estimate for the proportion of people who prefer spaghetti to linguini. 44. A study to compare French fries from McDonald’s with those from Burger King. Each subject was asked to eat two of each. a. Explain how randomization enters into the study design. b. Explain what “blind” means in the context of experimental design, and how it applies to this study. 45. The ability to grow in shade may help pines in the dry forests of Arizona resist drought. How well do these pines grow in shade? Investigators planted pine seedlings in a greenhouse in either full light or light reduced to 5% of normal by shade cloth. At the end of the study, they dried the young trees and weighed them. Identify the experimental units or subjects, the factors, and the response variables. Experimental units ____________________________________________ Factor(s) _________________________________ Response ______________________________________________ 46. Name the type of sampling employed in each of the following scenarios. a. There are seven sections of an introductory statistics course. A random sample of three sections is chosen and then random samples of 8 students from each of these sections are chosen. _____________________________ b. A student organization has 55 members. A table of random numbers is used to select a sample of 5. ________________________________________ c. An online poll asks people who visit this site to choose their favorite television show. ___________________________ d. Separate random samples of male and female first-year college students in an introductory psychology are selected to receive a one-week alternate instructional method. _____________________________________________ e. Which of the above sampling techniques would be considered poor due to possible bias? _______________________ 47. Explain what is wrong with each of the following sampling procedures and explain how you would do the randomization correctly. a. To determine the reading level of an introductory statistics text, you evaluate all the written material in the third chapter. b. You want to sample student opinions about a proposed change in procedures for changing majors. You hand out questionnaires to 100 students as they arrive for class at 7:30 A.M. c. A population of subjects is put in alphabetical order and a simple random sample of size 10 is taken by selecting the first 10 subjects in the list. 48. Mendelian genetics dictates that ratios of characteristics that are dominant vs. recessive occur as: Trait dominant1/dominant2 combination Proportion 9/16 dominant1/recessive2 dominant2/recessive1 recessive1/recessive2 3/16 3/16 1/16 An experiment produces the following numbers where “round” and “yellow” are dominant, “wrinkled” and “green” are recessive. Trait round yellow combination Count 315 312.75 round green wrinkled yellow wrinkled green 108 101 32 34.75 104.25 104.25 A. Find all expected counts and write them in the table above next to the observed counts. B. What kind of chi-square test is appropriate to test whether the data conform to the given Mendelian ratios? (Circle one) Goodness of Fit Independence C. Perform an appropriate chi-square test to determine whether the data conform to the given Mendelian ratios. 49. 8 Greek-Cypriot learners of English were randomly selected from all students of a particular program. Each was given an English sentence to translate, and each was scored by two teachers; one native English speaking teacher and one Greek teacher. The scores follow: English speaking teacher: 22 16 42 25 31 36 29 24 Greek teacher: 36 9 29 35 34 23 25 31 a. (7 pts) Calculate the mean difference for these students (English – Greek), and calculate the standard deviation of the differences. b. (8 pts) Make a graph of these differences, and use it to describe the distribution. c. (10 pts) Using the data above, we wish to determine whether the English teacher and the Greek teacher give similar scores. Choose an appropriate procedure to answer this question, and use it to answer the question clearly. 50. The following table shows the preferred transportation preferred by New York and Chicago citizens. Car Bus Bike Taxi Total Chicago 136 183 36 45 400 New York 164 217 64 155 600 Total 300 400 100 200 1000 Conduct an appropriate test to determine if location is related to transportation preference. 51. Time magazine reported the result of a telephone poll of 800 adult Americans. The question posed of the Americans who were surveyed was: "Should the federal tax on cigarettes be raised to pay for health care reform?" The results of the survey were: Non-smokers Smokers Number who said Yes 351 41 Number who said No 254 154 Conduct an appropriate test to determine whether the proportion of non-smokers who said yes differs from the proportion of smokers who said yes.
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Review questions for Final Exam
T/F

1. Height is an example of quantitative data.
Because height is a number which have decimals.
T / F 2. If data has a right (positively) skewed unimodal histogram, the median will be to the right of the mean.
No, because a positively skewed always has the mean to right of the median.
T / F 3. In a sample of size 25, the median is the average of the 12th and 13th largest values.
Yes, because the median is the middle value of an ordered data set. The middle value should be between
12th and 13th.
T / F 4. If the null hypothesis is not rejected, then we have proved that the null hypothesis is true.
We never can be 100% sure that the null hypothesis is true.
T / F 5. The p-value is the probability, assuming 𝐻0 is true, of obtaining a value of the test statistic higher than or
farther away from expected as what actually resulted.
T / F 6. If you toss a “fair” coin 100 times, you will observe exactly 50 heads.
The expected number of heads is 0 to 100 but it is not exactly 50 heads.
T / F 7. 𝑥̅ , s and σ are sample statistics.
The 𝑥̅ , s are sample statistics but σ is a population parameter.
T/F

𝜎

8. The margin of error 𝑧 ∗ ( 𝑛) of a confidence interval for 𝜇 decreases as n increases.


Yes, because the n is dividing the equation.
T / F 9. µ represents the sample mean.
No, µ represents the population mean.
T / F 10. In simple linear regression, if the null hypothesis is rejected in a test of 𝐻0 : 𝛽 = 0, there is a useful linear
relationship between x and y , so that values of x may help predict y.
T / F 11. In the simple linear regression model, 𝛽 ( the true slope of the regression line) can be interpreted as the
amount y will be expected to change when the value of the predictor variable x is increased by one unit.
The linear regression related the slope (𝛽) with the predictor variable x.
T / F 12. When a scatterplot is used to graph a bivariate data set, the variable plotted on the y-axis is the
response variable while the variable plotted on the x-axis is the predictor (explanatory) variable.
T / F 13. In hypothesis testing, a small p-value indicates that the observed sample results are inconsistent with
the null hypothesis.
T / F 14. The null hypothesis should be rejected when the p-value is larger than the significance level of the test.
We fail to reject the null hypothesis when p-value is larger than the significance level.
T / F 15. Two outcomes are independent if the chance that one outcome occurs is unaffected by knowledge of
whether or not the other occurred.
T / F 16. The mean is the middle value of an ordered data set.
No, the mean is the average of all values.
T / F 17. The 68-95-99.7 Rule can only be used when the data are approximately normal.
Yes, 1 standard deviation is 68%, 2 standard deviation is 95% and 3 standard deviation is 99.7%
T / F 18. s is the sample standard deviation.
True, the sample standard deviation is denoted by s and it is a sample statistic.
T / F 19. A z-score tells how many standard deviations a value is from the mean.
T / F 20. If the correlation coefficient r between x and y is 0, then there is no correlation seen between x and y.
Yes, when the correlation coefficient is equal to zero the is no correlation between the two variables.
T / F 21. A value of Pearson’s correlation coefficient r that is close to 1 indicates that there is a strong
relationship between two variables.
Yes, when the correlation coefficient is equal 1 indicates that there is a perfect relationship.

22. A manufacturer of cellular phones has decided that an assembly line is operating satisfactorily
if less than 3% of the phones produced per day are defective. To check the quality of a day's
production, the company decides to randomly sample 30 phones from a day's production to test
for defects. Define the population of interest to the manufacturer.
A. All the phones produced by the manufacturer.
C. The 30 responses: defective or not defective.

B. The 30 phones sampled and tested.
D. The 3% of the phones that are defective.

23. A manufacturer of cellular phones has decided that an assembly line is operating satisfactorily
if less than 3% of the phones produced per day are defective. To check the quality of a day's
production, the company decides to randomly sample 30 phones from a day's production to test
for defects. State the null and alternative hypotheses for a test.
A. 𝐻0 : 𝜇 = 0.03 vs. 𝐻𝑎 : 𝜇 > 0.03
C. 𝐻0 : 𝑝 = 0.03 vs. 𝐻𝑎 : 𝑝 < 0.03

B. 𝐻0 : 𝑝 = 0.03 vs. 𝐻𝑎 : 𝑝 > 0.03
D. 𝐻0 : 𝜇 = 0.03 vs. 𝐻𝑎 : 𝜇 < 0.03

𝑝 = 0.03 (3%)
24. For a random variable z which has a standard normal distribution, P(z < 2.10) =
a. 0.4821
b. 0.0179
c. 0.9821
d. none of these
From the z-tables:
𝑝(𝑧 < 2.10) = 0.9821
25. Suppose the random variable X has a normal distribution with mean 9.0 and variance 49.
The probability that X takes on a value of at least 18 is approximately equal to
a. 0.0985
b. 0.4286
c. 0.9015
d. correct approx. answer not given
𝑝(𝑥 ≥ 18) = 1 − 𝑝(𝑥 < 18)
18 − 9
𝑝(𝑥 ≥ 18) = 1 − 𝑝(𝑧 <
)
√49
𝑝(𝑥 ≥ 18) = 1 − 𝑝(𝑧 < 1.29)
𝑝(𝑥 ≥ 18) = 1 − 0.9015 = 0.0985
26. If the slope of the regression line is negative and the coefficient of determination (r-squared) is .64, then
the correlation coefficient is
a. 0.64
b. 0.8
c. -0.64
d. -0.8
As the regression line is negative the correlation coefficient is
𝑟 = −√0.64 = −0.8
27. The percentage of points falling below the 75th percentile is
a. 25%
b. 75%
c. can’t say
28. In a two-tailed test with calculated test statistic z = 1.68, the p-value is
a. .0930
b. .0465
c. .9170
d. .9535
𝑝(𝑧 > 1.68) = 0.04648

𝑝 − 𝑣𝑎𝑙𝑢𝑒 = 2 ∗ 𝑝 = 2 ∗ 0.04648 = 0.0930
29. The probability that a normal variable X falls within 2 standard deviations of the mean is
a. .0228
b. .9772
c. .0456
d. .9544
It is from the 68-95-99.7 Rule.
For problems 30 through 35, consider the following data set which consists of measurements of the daily emission
of sulfur oxides (in tons) for an industrial plant. { 15.8, 18.7, 6.2, 17.5, 11.0, 19.0, 26.4, 13.9, 14.7 }
30. What is n, the size of the sample?
a. 9
b. 10
c. 8

d. 143.20

31. What is 𝑥̅ , the sample mean?
a. 17.9
b. 15.91
c. 143.20

d. can’t say

e. can’t say

15.8 + 18.7 + 6.2 + 17.5 + 11.0 + 19.0 + 26.4 + 13.9 + 14.7
= 15.91
9
32. 𝑥̅ , the sample mean, and s, the sample standard deviation, are examples of
a. statistics
b. parameters
c. neither of these
𝑥̅ =

33. What is µ , the population mean?
a. 17.9
b. 15.91
c. 143.20

d. can’t say

34. Considering this sample of data provided, would you describe this data set as skewed? If so,
why? If not, why not?
The median is equal to 15.25
Since the mean is greater than median then, it is right skewed.

35. Find the 5-number summary and construct a boxplot for this sample.
Min= 6.2
Q1= 12.45
Mean=15.91
Q3= 18.1
Max= 26.4

36. Which of the following is a measure of the variability of a distribution?
A. Skewness
B. Median
C. Standard deviation

D. z-score

The measure of variability are range, variance and standard deviation.
37. Which of the following will reduce bias in a study?
I. A larger sample size.
II. A controlled experiment.
A. I and II

B. I and III

C. II and III

D. I, II & III

III. A random sample.
E. None of these.

38. Are Women Getting Taller? A researcher claims that the average height of a woman
aged 20 years or older is greater than the 1994 mean height of 63.7 inches, on the basis of
data obtained from the Centers for Disease Control and Prevention’s, Advance Data
Report, No. 347. She obtains a random sample of 45 women and finds the sample mean
height to be 63.9 inches. Assume that the population standard deviation is 3.5 inches.
Test the researcher’s claim at the 0.05 level of significance.
𝐻0 : μ = 63.7
𝐻0 : μ > 63.7
The level of significance, α = 0.05
Sample mean: 𝑥̅ = 63.9
Population standard deviation: 𝜎 = 3.5
The test statistic is,
𝑥̅ − 𝜇
𝜎
( )
√𝑛
63.9 − 63.7
𝑧=
3.5
(
)
√45
𝑧 = 0.3833
𝑧=

The p-value is,
𝑃 − 𝑣𝑎𝑙𝑢𝑒 = 1 − 𝑃(𝑧 < 0.3833)
𝑃 − 𝑣𝑎𝑙𝑢𝑒 = 1 − 0.6493 = 0.3507
As p-value = 0.3507 is greater than α = 0.05 we fail to reject the null hypothesis.
Conclusion: We cannot conclude that the average height of a woman aged 20 years or older is greater than the
1994 mean height of 63.7 inches.

39. For each of the population parameters, write the symbol for the corresponding sample

statistic, and the name of the statistic.
Sample estimate symbol
Sample estimate name
σ

__s____

__Sample standard deviation__________

µ

____𝑥̅ ___

__Sample mean_________________

p

____𝑝̂ ___

__Sample proportion__________

40. Make a back-to-ba...


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