SOPHIA STATISTICS UNIT 5 BUNDLED
QUESTIONS 2026 WITH COMPLETE
SOLUTIONS GRADED A+
◉ Amy works for a company that produces plastic lids and cups for
restaurants. She wants to use a one-sample z interval to estimate
what proportion of lids produced in a day have a defect that makes
them not fit the cups. She takes a random sample of 100 lids from
the more than 1,000 total lids produced that day and finds 5 lids in
the sample with this defect. Which conditions for constructing this
confidence interval did Amy's sample meet? Answer: The data is a
random sample from the population of interest.
Individual observations can be considered independent.
◉ A school administrator is curious what proportion of the 2,400
students at the school regularly eat breakfast. They take an SRS of
150 of these students, and 104 of them report that they regularly eat
breakfast. The administrator wants to use this data to construct a
one-sample z interval for a proportion. Which conditions for
constructing this confidence interval did their sample meet?
Answer: The data is a random sample from the population of
interest.
,The observed counts of successes and failures are both sufficiently
large.
Individual observations can be considered independent.
◉ Nkechi wants to use a one-sample z interval to estimate what
proportion of candies in a bag are red. She takes a random sample of
24 of the 80 total candies and finds that 18 of the candies in the
sample are red. Which conditions for constructing this confidence
interval did Nkechi's sample meet? Answer: The data is a random
sample from the population of interest.
◉ Elena wants to build a one-sample z interval to estimate what
proportion of computers produced at a factory have a certain defect.
She chooses a confidence level of 94%. A random sample of 200
computers shows that 12 computers have the defect. What critical
value z∗ should Elena use to construct this confidence interval?
Answer: z* = 1.88
◉ What is the critical value z∗ for constructing an 88% confidence
interval? Answer: z* = 1.555
◉ Elsie made a one-sample z interval for a proportion and used the
critical value z* = 1,405. What confidence level did she use? Answer:
84%
, ◉ Leandro wants to build a one-sample z interval with 98%
confidence to estimate the proportion of light bulbs that arrive
broken upon shipment to his store. He takes a random sample of 500
bulbs and finds that 25 arrived broken. What critical value z∗ should
Leandro use to construct this confidence interval? Answer: z* =
2.326
◉ What is the critical value z∗ for constructing an 80% confidence
interval? Answer: z* = 1.282
◉ Emer made a one-sample z interval for a proportion and used the
critical value z* = 1.476. What confidence level did she use? Answer:
86%
◉ Yun wants to build a one-sample z interval with 82% confidence
to estimate what proportion of users will click an advertisement that
appears on his website. He takes a random sample of 200 users and
finds that 34 of them clicked the advertisement. What critical value
z* should Yun use to construct this confidence interval? Answer: z* =
1.341
◉ What is the critical value z* for constructing a 95% confidence
interval? Answer: z* = 1.96
QUESTIONS 2026 WITH COMPLETE
SOLUTIONS GRADED A+
◉ Amy works for a company that produces plastic lids and cups for
restaurants. She wants to use a one-sample z interval to estimate
what proportion of lids produced in a day have a defect that makes
them not fit the cups. She takes a random sample of 100 lids from
the more than 1,000 total lids produced that day and finds 5 lids in
the sample with this defect. Which conditions for constructing this
confidence interval did Amy's sample meet? Answer: The data is a
random sample from the population of interest.
Individual observations can be considered independent.
◉ A school administrator is curious what proportion of the 2,400
students at the school regularly eat breakfast. They take an SRS of
150 of these students, and 104 of them report that they regularly eat
breakfast. The administrator wants to use this data to construct a
one-sample z interval for a proportion. Which conditions for
constructing this confidence interval did their sample meet?
Answer: The data is a random sample from the population of
interest.
,The observed counts of successes and failures are both sufficiently
large.
Individual observations can be considered independent.
◉ Nkechi wants to use a one-sample z interval to estimate what
proportion of candies in a bag are red. She takes a random sample of
24 of the 80 total candies and finds that 18 of the candies in the
sample are red. Which conditions for constructing this confidence
interval did Nkechi's sample meet? Answer: The data is a random
sample from the population of interest.
◉ Elena wants to build a one-sample z interval to estimate what
proportion of computers produced at a factory have a certain defect.
She chooses a confidence level of 94%. A random sample of 200
computers shows that 12 computers have the defect. What critical
value z∗ should Elena use to construct this confidence interval?
Answer: z* = 1.88
◉ What is the critical value z∗ for constructing an 88% confidence
interval? Answer: z* = 1.555
◉ Elsie made a one-sample z interval for a proportion and used the
critical value z* = 1,405. What confidence level did she use? Answer:
84%
, ◉ Leandro wants to build a one-sample z interval with 98%
confidence to estimate the proportion of light bulbs that arrive
broken upon shipment to his store. He takes a random sample of 500
bulbs and finds that 25 arrived broken. What critical value z∗ should
Leandro use to construct this confidence interval? Answer: z* =
2.326
◉ What is the critical value z∗ for constructing an 80% confidence
interval? Answer: z* = 1.282
◉ Emer made a one-sample z interval for a proportion and used the
critical value z* = 1.476. What confidence level did she use? Answer:
86%
◉ Yun wants to build a one-sample z interval with 82% confidence
to estimate what proportion of users will click an advertisement that
appears on his website. He takes a random sample of 200 users and
finds that 34 of them clicked the advertisement. What critical value
z* should Yun use to construct this confidence interval? Answer: z* =
1.341
◉ What is the critical value z* for constructing a 95% confidence
interval? Answer: z* = 1.96
