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I have got 50 questions, that need to be answered with a little explaining if possible ( like why you chose this ).
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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...