Score 22/24
You passed this Milestone
22 questions were answered correctly.
UNIT 5 — MILESTONE 5
2 questions were answered incorrectly.
1
Mrs. Pellegrin has weighed 5 packages of cheese and recorded the weights as 10.2 oz, 10.5 oz, 9.3 oz, 9.8 oz, and 10.0 oz. She calculated the
standard deviation to be 0.45 oz.
Select the 95% confidence interval for Mrs. Pellegrin's set of data.
9.4 to 10.52
9.53 to 10.39
9.34 to 10.44
9.48 to 10.44
RATIONALE
In order to get the 95% CI , we first need to find the critical t-score. Using a t-table, we need to find (n-1) degrees of freedom, or (5-1) = 4 df and
the corresponding CI
Using the 95% CI in the bottom row and 4 df on the far left column, we get a t-critical score of 2.776.
We also need to calculate the mean:
So we use the formula to find the confidence interval:
The lower bound is:
9.96 -0.56 = 9.40
The upper bound is:
9.96+0.56 = 10.52
CONCEPT
,Confidence Intervals Using the T-Distribution
2
A school is gathering some data on its sports teams because it was believed that the distribution of boys and girls were evenly distributed across all
the sports. This table lists the number of boys and girls participating in each sport.
Boys Girls
Tennis 18 30
Soccer 42 15
Swimming 12 18
Select the observed and expected frequencies for the boys participating in soccer.
Observed: 42
Expected: 24
Observed: 42
Expected: 22.5
Observed: 57
Expected: 22.5
Observed: 57
Expected: 24
RATIONALE
If we simply go to the chart then we can directly see the observed frequency for boys participating in soccer is 42.
To find the expected frequency, we need to find the number of
occurrences if the null hypothesis is true, which in this case, was that the three options are equally likely, or if the three options were all evenly
distributed.
First, add up all the options in the boys column:
If each of these three options were evenly distributed among the 72 boys, we would need to divide the total evenly between the three options:
This means we would expect 24 boys to choose tennis, 24 boys to choose soccer, and 24 boys to choose swimming.
CONCEPT
Chi-Square Statistic
3
What value of z* should be used to construct a 98% confidence interval of a population mean? Answer choices are rounded to the
thousandths place.
, 1.175
2.055
1.645
2.325
RATIONALE
Using the z-chart to construct a 98% CI, this means that there is 1% for each tail. The lower tail would be at 0.06 and the upper tail would be at (1
- 0.01) or 0.99. The closest to 0.94 on the z-table is between 0.9901 and 0.9898.
0.9898 corresponds with a z-score of 2.32.
0.9901 corresponds with a z-score of 2.33.
Taking the average of these two scores, we get a z-score of 2.325.
CONCEPT
Confidence Intervals
4
A table represents the number of students who passed or failed an aptitude test at two different campuses.
East Campus West Campus
Passed 39 45
Failed 61 55
You passed this Milestone
22 questions were answered correctly.
UNIT 5 — MILESTONE 5
2 questions were answered incorrectly.
1
Mrs. Pellegrin has weighed 5 packages of cheese and recorded the weights as 10.2 oz, 10.5 oz, 9.3 oz, 9.8 oz, and 10.0 oz. She calculated the
standard deviation to be 0.45 oz.
Select the 95% confidence interval for Mrs. Pellegrin's set of data.
9.4 to 10.52
9.53 to 10.39
9.34 to 10.44
9.48 to 10.44
RATIONALE
In order to get the 95% CI , we first need to find the critical t-score. Using a t-table, we need to find (n-1) degrees of freedom, or (5-1) = 4 df and
the corresponding CI
Using the 95% CI in the bottom row and 4 df on the far left column, we get a t-critical score of 2.776.
We also need to calculate the mean:
So we use the formula to find the confidence interval:
The lower bound is:
9.96 -0.56 = 9.40
The upper bound is:
9.96+0.56 = 10.52
CONCEPT
,Confidence Intervals Using the T-Distribution
2
A school is gathering some data on its sports teams because it was believed that the distribution of boys and girls were evenly distributed across all
the sports. This table lists the number of boys and girls participating in each sport.
Boys Girls
Tennis 18 30
Soccer 42 15
Swimming 12 18
Select the observed and expected frequencies for the boys participating in soccer.
Observed: 42
Expected: 24
Observed: 42
Expected: 22.5
Observed: 57
Expected: 22.5
Observed: 57
Expected: 24
RATIONALE
If we simply go to the chart then we can directly see the observed frequency for boys participating in soccer is 42.
To find the expected frequency, we need to find the number of
occurrences if the null hypothesis is true, which in this case, was that the three options are equally likely, or if the three options were all evenly
distributed.
First, add up all the options in the boys column:
If each of these three options were evenly distributed among the 72 boys, we would need to divide the total evenly between the three options:
This means we would expect 24 boys to choose tennis, 24 boys to choose soccer, and 24 boys to choose swimming.
CONCEPT
Chi-Square Statistic
3
What value of z* should be used to construct a 98% confidence interval of a population mean? Answer choices are rounded to the
thousandths place.
, 1.175
2.055
1.645
2.325
RATIONALE
Using the z-chart to construct a 98% CI, this means that there is 1% for each tail. The lower tail would be at 0.06 and the upper tail would be at (1
- 0.01) or 0.99. The closest to 0.94 on the z-table is between 0.9901 and 0.9898.
0.9898 corresponds with a z-score of 2.32.
0.9901 corresponds with a z-score of 2.33.
Taking the average of these two scores, we get a z-score of 2.325.
CONCEPT
Confidence Intervals
4
A table represents the number of students who passed or failed an aptitude test at two different campuses.
East Campus West Campus
Passed 39 45
Failed 61 55
