CNSL 503/CNSL 503 FINAL STATISTICS EXAM
2026/2027 WITH ACTUAL CORRECT
QUESTIONS AND VERIFIED DETAILED
ANSWERS |CURRENTLY TESTING
QUESTIONS AND SOLUTIONS|ALREADY
GRADED A+|NEWEST |BRAND NEW
VERSION|JUST RELEASED!!
which of the following are principles of the central limit theorem? Select all that apply.
- the mean of the distribution of sample means is equivalent to the population mean for larger
sample sizes
- the distribution of sample means is an approximately normal distribution for large sample sizes
- the median of the distribution of sample means is equal to 1
- the standard deviation of the distribution of sample means equals σ / √ n
- the distribution of samples means is a uniform distribution
-the mean of the distribution of sample means is equivalent to the population mean for larger
sample sizes
-the distribution of sample means is an approximately normal distribution for large sample sizes
-the standard deviation of the distribution of sample means equals σ / √ n
which of the following are some of the major critiques of hypothesis testing? select all that
apply.
- the significance level is an arbitrary value
- there is publishing bias towards results that are not statistically significant
- p values do not reflect the size of an effect
- hypothesis testing is unaffected by sample size
- the results of hypothesis testing are frequently misinterpreted and misunderstood
1|Page
,-the significance level is an arbitrary value
-p values do not reflect the size of an effect
-the results of hypothesis testing are frequently misinterpreted and misunderstood
Researchers are studying the relationship between room lighting and exam scores. After they
conduct their experiment, they find a statistically significant result that provides evidence that a
dimly lit room results in decreased performance on an exam. However, in reality, there is no
relationship between room lighting and exam performance. What type of error was made by
the researchers? Explain your answer.
Type 1 error - "false positive"
in this case the researchers rejected the null hypothesis when the null hypothesis was true
true or false: a normal distribution follows a symmetrical, bimodal curve
FALSE! a normal distribution follows a bell-shaped, symmetrical, UNIMODAL curve known as
"normal curve".
true or false: a normal distribution can be defined by its median
FALSE! but the mean is located in the middle of the curve and the median/mean/mode are
typically all equal.
true or false: a standard score is an exact value that is observed
false! a RAW SCORE is an exact value that is observed
The ____________ shows the proportion of values that fall to the left of a given z-score in a
normal distribution.
- normal curve
- t-table
- standard normal table
- normal frequency table
STANDARD NORMAL TABLE! Use the z-score to the nearest tenth
2|Page
,the _______________ hypothesis of a z-test states that there is no difference between a given
sample mean (x̄) and a population mean (μ). Whereas, the ____________ hypothesis states
there is a difference.
null; alternative
what does a z-score of 0 indicate?
the raw value corresponds to the mean
in my words: the raw value is the same number as the population mean (no deviation?)
what cohen's d value typically corresponds to a small effect size?
0.2
medium = 0.5
large = 0.8
in a normal distribution, approximately what percentage of values lie within 3 standard
deviations of the mean?
99.7% - the 68/95/99.7 rule says that 68% of the values fall within 1 standard deviation of the
mean, about 95% of the values fall within 2 standard deviations, and 99.7% of the values fall
within 3 standard deviations.
Jenna takes her male golden retriever to the vet for a yearly check-up. The dog's weight is 73
lbs. The average weight for a male golden retriever is 71 lbs with a standard deviation of 1.7 lbs.
Calculate the z-score for this value.
z=X-μ/σ
z score = sample value - population mean / standard deviation
= (73 - 71) / 1.7
= + 1.18
3|Page
, The customer service department of a technology company is rolling out a new protocol for
handling customer issues by allowing a few select representatives to try it out first. The average
customer satisfaction rating under the old protocol was 3.9 out of 5 (σ = 0.78) and the average
customer satisfaction rating under the new protocol is 4.1 out of 5. Calculate the effect size.
d = x̄ - μ / σ
= (4.1 - 3.9) / 0.78
= 0.26, small effect?
what calculation do researchers use to determine the absolute size of a treatment's effect
effect size (Cohens d)
Sabrina scored an 83 on both her economics and history exams. Her z-score for economics was
+1.27 and her z-score for history was -1.02. On which exam did she perform better? Explain
your answer.
She performed better on the economics exam. The positive z-score indicates a score above the
mean, whereas the negative z-score indicates a score below the mean.
which type of hypothesis test is also known as a directional test?
- one-tailed
- two-tailed
- predictive
- three tailed
one-tailed
For PE class, Jasmine's z-score for her time to run a mile was +0.7. The class average was 9.1 min
with a standard deviation of 1.1 min. How much time did it actually take Jasmine to run the
mile?
X = x̄ + z (s)
value = sample mean + z-score (standard deviation)
4|Page
2026/2027 WITH ACTUAL CORRECT
QUESTIONS AND VERIFIED DETAILED
ANSWERS |CURRENTLY TESTING
QUESTIONS AND SOLUTIONS|ALREADY
GRADED A+|NEWEST |BRAND NEW
VERSION|JUST RELEASED!!
which of the following are principles of the central limit theorem? Select all that apply.
- the mean of the distribution of sample means is equivalent to the population mean for larger
sample sizes
- the distribution of sample means is an approximately normal distribution for large sample sizes
- the median of the distribution of sample means is equal to 1
- the standard deviation of the distribution of sample means equals σ / √ n
- the distribution of samples means is a uniform distribution
-the mean of the distribution of sample means is equivalent to the population mean for larger
sample sizes
-the distribution of sample means is an approximately normal distribution for large sample sizes
-the standard deviation of the distribution of sample means equals σ / √ n
which of the following are some of the major critiques of hypothesis testing? select all that
apply.
- the significance level is an arbitrary value
- there is publishing bias towards results that are not statistically significant
- p values do not reflect the size of an effect
- hypothesis testing is unaffected by sample size
- the results of hypothesis testing are frequently misinterpreted and misunderstood
1|Page
,-the significance level is an arbitrary value
-p values do not reflect the size of an effect
-the results of hypothesis testing are frequently misinterpreted and misunderstood
Researchers are studying the relationship between room lighting and exam scores. After they
conduct their experiment, they find a statistically significant result that provides evidence that a
dimly lit room results in decreased performance on an exam. However, in reality, there is no
relationship between room lighting and exam performance. What type of error was made by
the researchers? Explain your answer.
Type 1 error - "false positive"
in this case the researchers rejected the null hypothesis when the null hypothesis was true
true or false: a normal distribution follows a symmetrical, bimodal curve
FALSE! a normal distribution follows a bell-shaped, symmetrical, UNIMODAL curve known as
"normal curve".
true or false: a normal distribution can be defined by its median
FALSE! but the mean is located in the middle of the curve and the median/mean/mode are
typically all equal.
true or false: a standard score is an exact value that is observed
false! a RAW SCORE is an exact value that is observed
The ____________ shows the proportion of values that fall to the left of a given z-score in a
normal distribution.
- normal curve
- t-table
- standard normal table
- normal frequency table
STANDARD NORMAL TABLE! Use the z-score to the nearest tenth
2|Page
,the _______________ hypothesis of a z-test states that there is no difference between a given
sample mean (x̄) and a population mean (μ). Whereas, the ____________ hypothesis states
there is a difference.
null; alternative
what does a z-score of 0 indicate?
the raw value corresponds to the mean
in my words: the raw value is the same number as the population mean (no deviation?)
what cohen's d value typically corresponds to a small effect size?
0.2
medium = 0.5
large = 0.8
in a normal distribution, approximately what percentage of values lie within 3 standard
deviations of the mean?
99.7% - the 68/95/99.7 rule says that 68% of the values fall within 1 standard deviation of the
mean, about 95% of the values fall within 2 standard deviations, and 99.7% of the values fall
within 3 standard deviations.
Jenna takes her male golden retriever to the vet for a yearly check-up. The dog's weight is 73
lbs. The average weight for a male golden retriever is 71 lbs with a standard deviation of 1.7 lbs.
Calculate the z-score for this value.
z=X-μ/σ
z score = sample value - population mean / standard deviation
= (73 - 71) / 1.7
= + 1.18
3|Page
, The customer service department of a technology company is rolling out a new protocol for
handling customer issues by allowing a few select representatives to try it out first. The average
customer satisfaction rating under the old protocol was 3.9 out of 5 (σ = 0.78) and the average
customer satisfaction rating under the new protocol is 4.1 out of 5. Calculate the effect size.
d = x̄ - μ / σ
= (4.1 - 3.9) / 0.78
= 0.26, small effect?
what calculation do researchers use to determine the absolute size of a treatment's effect
effect size (Cohens d)
Sabrina scored an 83 on both her economics and history exams. Her z-score for economics was
+1.27 and her z-score for history was -1.02. On which exam did she perform better? Explain
your answer.
She performed better on the economics exam. The positive z-score indicates a score above the
mean, whereas the negative z-score indicates a score below the mean.
which type of hypothesis test is also known as a directional test?
- one-tailed
- two-tailed
- predictive
- three tailed
one-tailed
For PE class, Jasmine's z-score for her time to run a mile was +0.7. The class average was 9.1 min
with a standard deviation of 1.1 min. How much time did it actually take Jasmine to run the
mile?
X = x̄ + z (s)
value = sample mean + z-score (standard deviation)
4|Page
