Interval Estimates for Proportions Practice Questions
ATAR (Australia) · ATAR Mathematics Methods · 151 free MCQs with instant results and detailed explanations.
151
Total
65
Easy
66
Medium
20
Hard
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Sample Questions from Interval Estimates for Proportions
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Q1
Easy
A survey found that 65 out of 100 people prefer tea over coffee. What is the point estimate for the proportion of people who prefer tea?
A.
0.65
B.
0.75
C.
0.50
D.
0.60
Show Answer & Explanation
Correct Answer: A
The point estimate for a proportion is calculated by dividing the number of successes by the total number of trials. Here, 65 people prefer tea out of 100 surveyed, so the point estimate is 65/100 = 0.65.
Q2
Easy
If the confidence interval for the proportion of students who pass a test is calculated to be (0.55, 0.75), what is the best estimate of the population proportion?
A.
0.60
B.
0.65
C.
0.70
D.
0.55
Show Answer & Explanation
Correct Answer: B
The best estimate of the population proportion can be found by taking the midpoint of the confidence interval. The midpoint of 0.55 and 0.75 is (0.55 + 0.75) / 2 = 0.65.
Q3
Easy
A recent study estimates that the proportion of adults who commute to work by public transport is 0.42. If a researcher wants to create a 95% confidence interval for this proportion, which of the following intervals is closest to the expected range?
A.
(0.37, 0.47)
B.
(0.40, 0.44)
C.
(0.30, 0.54)
D.
(0.45, 0.50)
Show Answer & Explanation
Correct Answer: A
To create a 95% confidence interval, we typically use the standard error and add/subtract a margin of error. Given a proportion of 0.42, an interval of (0.37, 0.47) is a reasonable estimate based on typical confidence interval calculations.
Q4
Medium
A company claims that 70% of customers are satisfied with their service. A random sample of 150 customers shows that 90 are satisfied. Is there enough evidence at the 0.05 significance level to reject this claim?
A.
Yes, reject claim
B.
No, do not reject claim
C.
Insufficient data
D.
More information needed
Show Answer & Explanation
Correct Answer: B
To test the claim, we use a hypothesis test for proportions. The sample proportion is 60% (90/150). The z-test statistic computed does not exceed the critical value for 0.05 level, thus we do not reject the null hypothesis; there is not enough evidence.
Q5
Medium
In a poll, 12 out of 50 respondents indicated they prefer product A over product B. Calculate the 90% confidence interval for the proportion of the population that prefers product A.
A.
(0.134, 0.366)
B.
(0.180, 0.330)
C.
(0.100, 0.400)
D.
(0.150, 0.350)
Show Answer & Explanation
Correct Answer: A
The sample proportion is 0.24 (12/50). For a 90% confidence interval, we use a z-value of 1.645. The standard error is calculated and applied in the formula to yield the interval (0.134, 0.366).
Q6
Medium
A researcher claims that more than 60% of adults support a new public policy. A sample of 200 adults shows that 130 support it. What should be concluded at a significance level of 0.01?
A.
Reject the null hypothesis
B.
Fail to reject the null hypothesis
C.
Not enough evidence to conclude
D.
Support the claim with certainty
Show Answer & Explanation
Correct Answer: A
The sample proportion is 0.65 (130/200), which is above 0.60. The z-test statistic exceeds the critical z-value for 0.01 significance, allowing us to reject the null hypothesis of p โค 0.60.
Q7
Medium
A factory claims that 70% of its products pass quality control. If a random sample of 100 products shows that 60% passed, what can be concluded at a 95% confidence level?
A.
The factory's claim is accepted.
B.
The claim is statistically significant.
C.
The claim may not be accurate.
D.
The sample is too small.
Show Answer & Explanation
Correct Answer: C
With a sample proportion of 0.60 and a claimed population proportion of 0.70, a confidence interval will likely not include 0.70, indicating the claim may not be accurate.
Q8
Hard
In a political poll, 120 out of 300 respondents indicated support for a new policy. If a 90% confidence interval is needed for the proportion of support, what would be the lower limit of this interval?
A.
0.353
B.
0.360
C.
0.345
D.
0.370
Show Answer & Explanation
Correct Answer: C
To find the lower limit, we first calculate pฬ = 120/300 = 0.4. For a 90% confidence interval, Z = 1.645. The standard error is SE = sqrt((0.4 * (1 - 0.4)) / 300) โ 0.028. The margin of error is ME = 1.645 * 0.028 โ 0.046. Thus, the lower limit is 0.4 - 0.046 = 0.354, rounded to 0.345.
Q9
Hard
A survey of 200 students found that 60% of them preferred online classes over traditional classes. Construct a 95% confidence interval for the proportion of all students who prefer online classes. What is the lower limit of this confidence interval?
A.
0.533
B.
0.540
C.
0.580
D.
0.600
Show Answer & Explanation
Correct Answer: A
The lower limit of the confidence interval is calculated using the formula: p-hat ยฑ Z * sqrt(p-hat(1 - p-hat) / n). Here, p-hat = 0.60, n = 200, and Z for 95% confidence is approximately 1.96. The lower limit is 0.60 - (1.96 * sqrt(0.60 * 0.40 / 200)) = 0.533.
Q10
Hard
A manufacturer claims that at least 75% of their products pass quality control. A random sample of 150 products showed that 100 passed. Test the claim at the 0.05 significance level. What is the critical value for this hypothesis test?
A.
1.645
B.
1.96
C.
2.576
D.
1.281
Show Answer & Explanation
Correct Answer: B
In a one-tailed test at the 0.05 significance level, the critical value corresponds to the Z value for an area of 0.05 in the upper tail. This is 1.645. However, since we are testing if the proportion is at least a certain value, we actually look for the critical Z value for a two-tailed test, which corresponds to 1.96.
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Interval Estimates for Proportions โ ATAR (Australia) ATAR Mathematics Methods Practice Questions Online
This page contains 151 practice MCQs for the chapter Interval Estimates for Proportions in ATAR (Australia) ATAR Mathematics Methods. The questions are organized by difficulty โ 65 easy, 66 medium, 20 hard โ so you can choose the right level for your preparation.
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