MATH 1680/ 317 Qs with Certified Ans/ 2025
What is at the "heart" of hypothesis testing in statistics? - Answer: Make an assumption about reality,
and collect sample evidence to determine whether it contradicts the assumption.
What is a hypothesis? - Answer: A statement regarding a characteristic of one or more populations.
Why do we test statements about a population parameter using sample data? - Answer: Because it is
usually impossible or impractical to gain access to the entire population.
The 95% in a 95% confidence interval represents the proportion of all samples that will result in intervals
that include the population proportion. - Answer: In practice, we construct only one confidence interval
based on one sample. We do not know whether the sample results in a confidence interval that includes
the parameter, but we do know that if we construct a 95% confidence interval, it will include the
unknown parameter 95% of the time.
As the level of confidence increases, what happens to the critical value? - Answer: It increases
Page 1 of 41
,List the critical value associated with the given level of confidence. - Answer: A) 90% : 1.645 B) 95% :
1.96 C) 99% : 2.575
State the interpretation of a confidence interval. - Answer: A (1−α)⋅100% confidence interval indicates
that (1−α)⋅100% of all simple random samples of size n from the population whose parameter is
unknown will result in an interval that contains the parameter.
Constructing a Confidence Interval for a Population Proportion using StatCrunch - Answer: - Stat >
proportion stats > one sample > with summary
-Enter number of successes (x) and number of observations (n)
- Choose the confidence interval radio button, enter the level of confidence (leave method as Standard-
Wald)
- Click compute
As the sample size, n, increases, what happens to the margin of error? - Answer: As the sample size, n,
increases, the margin of error decreases. Therefore, larger sample sizes will result in narrower
confidence intervals.
If the sample size is quadrupled, the margin of error will be cut in half. - Answer: True
If the normality condition is not satisfied, how does the proportion of intervals that capture the
parameter compare to the level of confidence? - Answer: When the normality condition is not satisfied,
the proportion of intervals that capture the parameter is below the level of confidence.
If the normality requirement is not satisfied (that is, np(1−p) is not at least 10), then a 95% confidence
interval about the population proportion will include the population proportion in ________ 95% of the
intervals. - Answer: less than
What is the point estimate for a population mean mu? - Answer: The sample mean x-
Page 2 of 41
,What was the name of the brewery that Gosset worked for? What pseudonym did he choose to publish
his results about a model that accounts for the additional variability introduced by using s in place of
when determining margin of error? - Answer: The Guinness Brewery.
Chose Student as his pseudonym
State six properties of the t-distribution. - Answer: 1. The t distribution is different for different degrees
of freedom
2. The t distribution is centered at 0 and is symmetric about 0
3. The area under the curve is 1. The area under the curve to the right of 0 equals the area under the
curve to the left of 0 which equals 1/2
4. As t increases or decreases without bound, the graph approaches, but never equals 0
5. The area in the tails of the t-distribution is a little greater than the area in the tails of the standard
normal distribution, because we are using s as an estimate of sigma, thereby introducing further
variability into the t-statistic
6. As the sample size n increases, the density curve of t gets closer to the standard normal density curve.
This result occurs because, as the sample size increases, the values of s get closer to the value of sigma,
by the Law of Large Numbers
Put the following in order for the most area in the tails of the distribution.
(a) Standard Normal Distribution
(b) Student's t-Distribution with 15 degrees of freedom.
(c) Student's t-Distribution with 30 degrees of freedom. - Answer: b, c, a
State the definition of hypothesis testing. - Answer: A procedure based on sample evidence and
probability, used to test statements regarding a characteristic of one or more populations.
List the 3 steps in hypothesis testing. - Answer: 1. Make a statement regarding the nature of the
population.
2. Collect evidence (sample data) to test the statement
3. Analyze the data to assess the plausibility of the statement
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, State the definition of the null hypothesis. - Answer: A statement to be tested. The null hypothesis is a
statement of no change, no effect, or no difference and is assumed true until evidence indicates
otherwise.
List the three ways to set up the null and alternative hypotheses. - Answer: Two tailed test
Equal versus not equal hypothesis
H0 : parameter = some value
H1 : parameter does not equal some value
Left-tailed test
2. Equal versus less than
H0 : parameter = some value
H1 : parameter < some value
Right-tailed test
3. Equal versus greater than
H0 : parameter = some value
H1 : parameter > some value
What type of tests are referred to as one-tailed tests? - Answer: Left and right tailed tests
What determines the structure of the alternative hypothesis (two-tailed, left-tailed, or right-tailed?) -
Answer: The statement we are trying to gather evidence for.
What type of error is called a Type I error? - Answer: Reject the null hypothesis when the null hypothesis
is true. This decision would be incorrect. This type of error is called a Type I error.
What type of error is called a Type II error? - Answer: Do not reject the null hypothesis when the
alternative hypothesis is true. This decision would be incorrect. This type of error is called a Type II error.
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What is at the "heart" of hypothesis testing in statistics? - Answer: Make an assumption about reality,
and collect sample evidence to determine whether it contradicts the assumption.
What is a hypothesis? - Answer: A statement regarding a characteristic of one or more populations.
Why do we test statements about a population parameter using sample data? - Answer: Because it is
usually impossible or impractical to gain access to the entire population.
The 95% in a 95% confidence interval represents the proportion of all samples that will result in intervals
that include the population proportion. - Answer: In practice, we construct only one confidence interval
based on one sample. We do not know whether the sample results in a confidence interval that includes
the parameter, but we do know that if we construct a 95% confidence interval, it will include the
unknown parameter 95% of the time.
As the level of confidence increases, what happens to the critical value? - Answer: It increases
Page 1 of 41
,List the critical value associated with the given level of confidence. - Answer: A) 90% : 1.645 B) 95% :
1.96 C) 99% : 2.575
State the interpretation of a confidence interval. - Answer: A (1−α)⋅100% confidence interval indicates
that (1−α)⋅100% of all simple random samples of size n from the population whose parameter is
unknown will result in an interval that contains the parameter.
Constructing a Confidence Interval for a Population Proportion using StatCrunch - Answer: - Stat >
proportion stats > one sample > with summary
-Enter number of successes (x) and number of observations (n)
- Choose the confidence interval radio button, enter the level of confidence (leave method as Standard-
Wald)
- Click compute
As the sample size, n, increases, what happens to the margin of error? - Answer: As the sample size, n,
increases, the margin of error decreases. Therefore, larger sample sizes will result in narrower
confidence intervals.
If the sample size is quadrupled, the margin of error will be cut in half. - Answer: True
If the normality condition is not satisfied, how does the proportion of intervals that capture the
parameter compare to the level of confidence? - Answer: When the normality condition is not satisfied,
the proportion of intervals that capture the parameter is below the level of confidence.
If the normality requirement is not satisfied (that is, np(1−p) is not at least 10), then a 95% confidence
interval about the population proportion will include the population proportion in ________ 95% of the
intervals. - Answer: less than
What is the point estimate for a population mean mu? - Answer: The sample mean x-
Page 2 of 41
,What was the name of the brewery that Gosset worked for? What pseudonym did he choose to publish
his results about a model that accounts for the additional variability introduced by using s in place of
when determining margin of error? - Answer: The Guinness Brewery.
Chose Student as his pseudonym
State six properties of the t-distribution. - Answer: 1. The t distribution is different for different degrees
of freedom
2. The t distribution is centered at 0 and is symmetric about 0
3. The area under the curve is 1. The area under the curve to the right of 0 equals the area under the
curve to the left of 0 which equals 1/2
4. As t increases or decreases without bound, the graph approaches, but never equals 0
5. The area in the tails of the t-distribution is a little greater than the area in the tails of the standard
normal distribution, because we are using s as an estimate of sigma, thereby introducing further
variability into the t-statistic
6. As the sample size n increases, the density curve of t gets closer to the standard normal density curve.
This result occurs because, as the sample size increases, the values of s get closer to the value of sigma,
by the Law of Large Numbers
Put the following in order for the most area in the tails of the distribution.
(a) Standard Normal Distribution
(b) Student's t-Distribution with 15 degrees of freedom.
(c) Student's t-Distribution with 30 degrees of freedom. - Answer: b, c, a
State the definition of hypothesis testing. - Answer: A procedure based on sample evidence and
probability, used to test statements regarding a characteristic of one or more populations.
List the 3 steps in hypothesis testing. - Answer: 1. Make a statement regarding the nature of the
population.
2. Collect evidence (sample data) to test the statement
3. Analyze the data to assess the plausibility of the statement
Page 3 of 41
, State the definition of the null hypothesis. - Answer: A statement to be tested. The null hypothesis is a
statement of no change, no effect, or no difference and is assumed true until evidence indicates
otherwise.
List the three ways to set up the null and alternative hypotheses. - Answer: Two tailed test
Equal versus not equal hypothesis
H0 : parameter = some value
H1 : parameter does not equal some value
Left-tailed test
2. Equal versus less than
H0 : parameter = some value
H1 : parameter < some value
Right-tailed test
3. Equal versus greater than
H0 : parameter = some value
H1 : parameter > some value
What type of tests are referred to as one-tailed tests? - Answer: Left and right tailed tests
What determines the structure of the alternative hypothesis (two-tailed, left-tailed, or right-tailed?) -
Answer: The statement we are trying to gather evidence for.
What type of error is called a Type I error? - Answer: Reject the null hypothesis when the null hypothesis
is true. This decision would be incorrect. This type of error is called a Type I error.
What type of error is called a Type II error? - Answer: Do not reject the null hypothesis when the
alternative hypothesis is true. This decision would be incorrect. This type of error is called a Type II error.
Page 4 of 41
