1/19/2021 Sophia :: Welcome
Score 24/24
You passed this Milestone
24 questions were answered correctly.
UNIT 5 — MILESTONE 5
1
Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the
population standard deviation is 0.1 inch.
To see if the batch of screws has a significantly different mean length from 3 inches, what would the value
of the z-test statistic be?
-10
1
10
-1
RATIONALE
If we first note the denominator of
Then, getting the z-score we can note it is
https://strayer.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/7564141 1/23
,1/19/2021 Sophia :: Welcome
This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.
CONCEPT
Z-Test for Population Means
2
The data below shows the grams of fat in a series of popular snacks.
Snack Grams of Fat
Snack 1 9
Snack 2 13
Snack 3 21
Snack 4 30
Snack 5 31
Snack 6 31
Snack 7 34
Snack 8 25
Snack 9 28
Snack 10 20
If Morris wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom
be?
11
10
9
5
RATIONALE
The degrees of freedom for a 1 sample t-test are df=n-1 where n is the sample size. In this case, n=10, then df =
n-1 = 10-1 = 9.
CONCEPT
https://strayer.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/7564141 2/23
, 1/19/2021 Sophia :: Welcome
T-Tests
3
A market research company conducted a survey to find the level of affluence in a city. They defined the category
"affluence" for people earning $100,000 or more annually. Out of 267 persons who replied to their survey, 32 are
considered affluent.
What is the 95% confidence interval for this population proportion? Answer choices are rounded to the
hundredths place.
0.08 to 0.16
0.08 to 0.34
0.24 to 0.34
0.16 to 0.24
RATIONALE
In order to get the CI we want to use the following form.
p with hat on top plus-or-minus z to the power of asterisk times square root of fraction numerator
p with hat on top q with hat on top over denominator n end fraction end root
First, we must determine the corresponding z*score for 95% Confidence Interval. Remember, this means that
we have 2.5% for the tails, meaning 2.5%, or 0.025, for each tail. Using a z-table, we can find the upper
z-score by finding (1 - 0.025) or 0.975 in the table.
This corresponding z-score is at 1.96.
We can know
So putting it together:
https://strayer.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/7564141 3/23
Score 24/24
You passed this Milestone
24 questions were answered correctly.
UNIT 5 — MILESTONE 5
1
Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the
population standard deviation is 0.1 inch.
To see if the batch of screws has a significantly different mean length from 3 inches, what would the value
of the z-test statistic be?
-10
1
10
-1
RATIONALE
If we first note the denominator of
Then, getting the z-score we can note it is
https://strayer.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/7564141 1/23
,1/19/2021 Sophia :: Welcome
This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.
CONCEPT
Z-Test for Population Means
2
The data below shows the grams of fat in a series of popular snacks.
Snack Grams of Fat
Snack 1 9
Snack 2 13
Snack 3 21
Snack 4 30
Snack 5 31
Snack 6 31
Snack 7 34
Snack 8 25
Snack 9 28
Snack 10 20
If Morris wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom
be?
11
10
9
5
RATIONALE
The degrees of freedom for a 1 sample t-test are df=n-1 where n is the sample size. In this case, n=10, then df =
n-1 = 10-1 = 9.
CONCEPT
https://strayer.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/7564141 2/23
, 1/19/2021 Sophia :: Welcome
T-Tests
3
A market research company conducted a survey to find the level of affluence in a city. They defined the category
"affluence" for people earning $100,000 or more annually. Out of 267 persons who replied to their survey, 32 are
considered affluent.
What is the 95% confidence interval for this population proportion? Answer choices are rounded to the
hundredths place.
0.08 to 0.16
0.08 to 0.34
0.24 to 0.34
0.16 to 0.24
RATIONALE
In order to get the CI we want to use the following form.
p with hat on top plus-or-minus z to the power of asterisk times square root of fraction numerator
p with hat on top q with hat on top over denominator n end fraction end root
First, we must determine the corresponding z*score for 95% Confidence Interval. Remember, this means that
we have 2.5% for the tails, meaning 2.5%, or 0.025, for each tail. Using a z-table, we can find the upper
z-score by finding (1 - 0.025) or 0.975 in the table.
This corresponding z-score is at 1.96.
We can know
So putting it together:
https://strayer.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/7564141 3/23
