IDS 270 BUSINESS STATISTICS FINAL EXAMINATION
| COMPLETE SOLUTIONS | VERIFIED QUESTIONS &
ANSWERS | LATEST UPDATE 2026/2027 | ACTUAL
EXAM | PRACTICE QUESTIONS AND ANSWERS |
EXAM REVIEW | 100% CORRECT ANSWERS |
VERIFIED SOLUTIONS
This comprehensive final examination preparation document has been
meticulously developed for students enrolled in IDS 270: Business Statistics. This
100-question assessment comprehensively covers the statistical concepts and
analytical techniques essential for business decision-making, including descriptive
statistics and data visualization, probability theory and probability distributions,
sampling distributions and statistical inference, hypothesis testing and confidence
intervals, regression analysis and correlation, time series analysis and forecasting,
analysis of variance and experimental design, and nonparametric statistical
methods. Each question has been crafted to reflect the rigorous analytical
standards of business statistics education, emphasizing quantitative reasoning,
appropriate selection and application of statistical methods, accurate
interpretation of statistical output, and the communication of statistical findings to
support evidence-based business decisions. This study resource serves as an
essential tool for students seeking to master the application of statistical reasoning
to business problems.
Table of Contents:
1.0 Descriptive Statistics and Data Visualization
2.0 Probability Theory and Probability Distributions
3.0 Sampling Distributions and Confidence Intervals
4.0 Hypothesis Testing: One-Sample and Two-Sample Tests
5.0 Analysis of Variance and Experimental Design
6.0 Regression Analysis and Correlation
7.0 Time Series Analysis and Business Forecasting
8.0 Nonparametric Methods and Categorical Data Analysis
,Question 1: A business analyst collects data on the annual salaries (in thousands of
dollars) of 15 employees at a small firm: 42, 45, 48, 50, 52, 55, 55, 58, 60, 62, 65,
68, 70, 72, 250. The analyst is asked to report the "typical" salary. Which measure
of central tendency is MOST appropriate for this data set, and why?
A) The mean, because it uses all observations in its calculation and is the most
commonly reported measure of central tendency
B) The median, because the data set contains an extreme outlier ($250,000) that
substantially inflates the mean. The mean salary would be approximately $70,133,
which is higher than 13 of the 15 salaries and does not accurately represent the
typical salary. The median salary of $58,000 is unaffected by the outlier and
provides a more accurate representation of central tendency for skewed data
C) The mode, because it represents the most frequently occurring value
D) The range, because it captures the spread of the data
Correct Answer: B
The data set is right-skewed due to the presence of an extreme outlier ($250,000,
which may be the owner's salary). The mean is highly sensitive to extreme values:
the mean of $70,133 is greater than 13 of the 15 salaries (all except $70,000,
$72,000, and $250,000) and does not represent the typical employee salary. The
median ($58,000) is resistant to outliers and provides a more accurate measure of
central tendency for skewed distributions. This example illustrates why the median
is preferred over the mean for income data, which is typically right-skewed. The
mode ($55,000, occurring twice) is also unaffected but provides less information.
This is a fundamental principle in descriptive statistics: the choice of central
tendency measure should be informed by the distribution's shape.
Question 2: A manufacturing process produces steel rods with diameters that
follow a normal distribution with a mean of 10.00 millimeters and a standard
deviation of 0.05 millimeters. The specification limits for the rods are 9.90 mm to
10.10 mm. What proportion of the rods produced will fall within the specification
limits?
A) Approximately 68.27%
B) Approximately 95.45%
C) Approximately 99.73%
D) Approximately 90.00%
Correct Answer: B
The specification limits are 9.90 mm and 10.10 mm. Calculate the z-scores: Lower
, limit z = (9.90 - 10.00) / 0.05 = -2.00. Upper limit z = (10.10 - 10.00) / 0.05 =
+2.00. For a standard normal distribution, the area between z = -2.00 and z =
+2.00 is approximately 95.45% (more precisely, using the empirical rule,
approximately 95% of observations fall within 2 standard deviations of the mean).
This means approximately 95.45% of the rods produced will meet specifications,
and approximately 4.55% will be defective (outside the specification limits). This
calculation uses the normal distribution to assess process capability—a
fundamental application of statistics in quality control.
Question 3: A marketing researcher wants to estimate the proportion of consumers
who recognize a brand logo. A random sample of 400 consumers is surveyed, and
220 recognize the logo. Construct a 95% confidence interval for the true
population proportion.
A) (0.50, 0.60)
B) (0.501, 0.599)
C) (0.473, 0.627)
D) (0.55, 0.55)
Correct Answer: B
Sample proportion p̂ = 220/400 = 0.55. For a 95% confidence interval, z = 1.96.
Standard error of the proportion = sqrt[p̂(1 - p̂) / n] = sqrt[(0.55 × 0.45) / 400] =
sqrt[0.] = sqrt[0.00061875] = 0.02487. Margin of error = z* × SE = 1.96
× 0.02487 = 0.04875. Confidence interval = p̂ ± margin of error = 0.55 ± 0.04875
= (0.50125, 0.59875), rounded to (0.501, 0.599). Interpretation: We are 95%
confident that the true proportion of consumers who recognize the brand logo is
between 50.1% and 59.9%. The margin of error is approximately 4.9 percentage
points.*
Question 4: A company claims that the mean lifetime of its batteries is 50 hours.
A consumer protection agency tests a random sample of 36 batteries and finds a
sample mean lifetime of 48.2 hours with a sample standard deviation of 5.4 hours.
Test the company's claim at the α = 0.05 significance level. What is the appropriate
conclusion?
A) Reject the null hypothesis; there is sufficient evidence that the mean lifetime is
less than 50 hours
B) Fail to reject the null hypothesis; there is insufficient evidence to contradict the
company's claim
| COMPLETE SOLUTIONS | VERIFIED QUESTIONS &
ANSWERS | LATEST UPDATE 2026/2027 | ACTUAL
EXAM | PRACTICE QUESTIONS AND ANSWERS |
EXAM REVIEW | 100% CORRECT ANSWERS |
VERIFIED SOLUTIONS
This comprehensive final examination preparation document has been
meticulously developed for students enrolled in IDS 270: Business Statistics. This
100-question assessment comprehensively covers the statistical concepts and
analytical techniques essential for business decision-making, including descriptive
statistics and data visualization, probability theory and probability distributions,
sampling distributions and statistical inference, hypothesis testing and confidence
intervals, regression analysis and correlation, time series analysis and forecasting,
analysis of variance and experimental design, and nonparametric statistical
methods. Each question has been crafted to reflect the rigorous analytical
standards of business statistics education, emphasizing quantitative reasoning,
appropriate selection and application of statistical methods, accurate
interpretation of statistical output, and the communication of statistical findings to
support evidence-based business decisions. This study resource serves as an
essential tool for students seeking to master the application of statistical reasoning
to business problems.
Table of Contents:
1.0 Descriptive Statistics and Data Visualization
2.0 Probability Theory and Probability Distributions
3.0 Sampling Distributions and Confidence Intervals
4.0 Hypothesis Testing: One-Sample and Two-Sample Tests
5.0 Analysis of Variance and Experimental Design
6.0 Regression Analysis and Correlation
7.0 Time Series Analysis and Business Forecasting
8.0 Nonparametric Methods and Categorical Data Analysis
,Question 1: A business analyst collects data on the annual salaries (in thousands of
dollars) of 15 employees at a small firm: 42, 45, 48, 50, 52, 55, 55, 58, 60, 62, 65,
68, 70, 72, 250. The analyst is asked to report the "typical" salary. Which measure
of central tendency is MOST appropriate for this data set, and why?
A) The mean, because it uses all observations in its calculation and is the most
commonly reported measure of central tendency
B) The median, because the data set contains an extreme outlier ($250,000) that
substantially inflates the mean. The mean salary would be approximately $70,133,
which is higher than 13 of the 15 salaries and does not accurately represent the
typical salary. The median salary of $58,000 is unaffected by the outlier and
provides a more accurate representation of central tendency for skewed data
C) The mode, because it represents the most frequently occurring value
D) The range, because it captures the spread of the data
Correct Answer: B
The data set is right-skewed due to the presence of an extreme outlier ($250,000,
which may be the owner's salary). The mean is highly sensitive to extreme values:
the mean of $70,133 is greater than 13 of the 15 salaries (all except $70,000,
$72,000, and $250,000) and does not represent the typical employee salary. The
median ($58,000) is resistant to outliers and provides a more accurate measure of
central tendency for skewed distributions. This example illustrates why the median
is preferred over the mean for income data, which is typically right-skewed. The
mode ($55,000, occurring twice) is also unaffected but provides less information.
This is a fundamental principle in descriptive statistics: the choice of central
tendency measure should be informed by the distribution's shape.
Question 2: A manufacturing process produces steel rods with diameters that
follow a normal distribution with a mean of 10.00 millimeters and a standard
deviation of 0.05 millimeters. The specification limits for the rods are 9.90 mm to
10.10 mm. What proportion of the rods produced will fall within the specification
limits?
A) Approximately 68.27%
B) Approximately 95.45%
C) Approximately 99.73%
D) Approximately 90.00%
Correct Answer: B
The specification limits are 9.90 mm and 10.10 mm. Calculate the z-scores: Lower
, limit z = (9.90 - 10.00) / 0.05 = -2.00. Upper limit z = (10.10 - 10.00) / 0.05 =
+2.00. For a standard normal distribution, the area between z = -2.00 and z =
+2.00 is approximately 95.45% (more precisely, using the empirical rule,
approximately 95% of observations fall within 2 standard deviations of the mean).
This means approximately 95.45% of the rods produced will meet specifications,
and approximately 4.55% will be defective (outside the specification limits). This
calculation uses the normal distribution to assess process capability—a
fundamental application of statistics in quality control.
Question 3: A marketing researcher wants to estimate the proportion of consumers
who recognize a brand logo. A random sample of 400 consumers is surveyed, and
220 recognize the logo. Construct a 95% confidence interval for the true
population proportion.
A) (0.50, 0.60)
B) (0.501, 0.599)
C) (0.473, 0.627)
D) (0.55, 0.55)
Correct Answer: B
Sample proportion p̂ = 220/400 = 0.55. For a 95% confidence interval, z = 1.96.
Standard error of the proportion = sqrt[p̂(1 - p̂) / n] = sqrt[(0.55 × 0.45) / 400] =
sqrt[0.] = sqrt[0.00061875] = 0.02487. Margin of error = z* × SE = 1.96
× 0.02487 = 0.04875. Confidence interval = p̂ ± margin of error = 0.55 ± 0.04875
= (0.50125, 0.59875), rounded to (0.501, 0.599). Interpretation: We are 95%
confident that the true proportion of consumers who recognize the brand logo is
between 50.1% and 59.9%. The margin of error is approximately 4.9 percentage
points.*
Question 4: A company claims that the mean lifetime of its batteries is 50 hours.
A consumer protection agency tests a random sample of 36 batteries and finds a
sample mean lifetime of 48.2 hours with a sample standard deviation of 5.4 hours.
Test the company's claim at the α = 0.05 significance level. What is the appropriate
conclusion?
A) Reject the null hypothesis; there is sufficient evidence that the mean lifetime is
less than 50 hours
B) Fail to reject the null hypothesis; there is insufficient evidence to contradict the
company's claim
