Mock Quiz Hub
Dark
Mock Quiz Hub
1
Recent Updates
Added: OS Mid 1 Quiz
Added: OS Mid 2 Quiz
Added: OS Lab 1 Quiz
Check back for more updates!
Time: 00:00
Quiz
Navigate through questions using the controls below
0%
Question 1 of 40
Quiz ID: q1
A 95% confidence interval for the mean breakdown voltage of an insulator is calculated from a sample to be (42.1 kV, 47.9 kV). What is the correct interpretation of this interval?
95% of all insulators have a breakdown voltage between 42.1 kV and 47.9 kV.
We are 95% confident that the true population mean breakdown voltage lies between 42.1 kV and 47.9 kV.
There is a 95% probability that the sample mean is between 42.1 kV and 47.9 kV.
The sample mean is exactly 45.0 kV.
Question 2 of 40
Quiz ID: q2
The general form of a confidence interval is 'Statistic ± Margin of Error'. If the margin of error for a population mean is 5.2 and the sample mean is 80.0, what is the confidence interval?
(74.8, 85.2)
(75.0, 85.0)
(80.0, 85.2)
(5.2, 80.0)
Question 3 of 40
Quiz ID: q3
What is the standard error (SE) for the sample mean?
s / n
s² / √n
s / √n
σ / √n
Question 4 of 40
Quiz ID: q4
To construct a 99% confidence interval for a population proportion, you would use a critical Z-value (Z_(α/2)) of approximately:
1.96
1.645
2.576
2.326
Question 5 of 40
Quiz ID: q5
The standard error for the difference between two independent sample means, x̄₁ - x̄₂, is:
s₁/n₁ + s₂/n₂
√(s₁²/n₁ + s₂²/n₂)
(s₁ + s₂)/√(n₁ + n₂)
√(s_p²(1/n₁ + 1/n₂))
Question 6 of 40
Quiz ID: q6
A poll of 500 voters shows 55% support a candidate. What is the standard error for this sample proportion?
√(0.55*0.45/500)
0.55/√500
√(0.55/500)
0.55*0.45/500
Question 7 of 40
Quiz ID: q7
Which distribution is used to construct a confidence interval for a population variance (σ²)?
The normal (Z) distribution
The t-distribution
The Chi-square (χ²) distribution
The F-distribution
Question 8 of 40
Quiz ID: q8
The formula for a CI for variance is [(n-1)s² / χ²₁₋α/₂, (n-1)s² / χ²α/₂]. For a 95% CI with n=17, what are the correct degrees of freedom for the Chi-square values?
16
17
n
2
Question 9 of 40
Quiz ID: q9
For a 95% CI for variance, the Chi-square values χ²α/₂ and χ²₁₋α/₂ are chosen so that:
2.5% of the area is in each tail of the distribution.
5% of the area is in each tail of the distribution.
5% of the area is in the right tail only.
95% of the area is between them.
Question 10 of 40
Quiz ID: q10
From the computational exercise: n=17, s²=137324.3. To find the 95% CI for σ², you need Chi-square values. If χ²₀.₀₂₅,₁₆ = 28.845 and χ²₀.₉₇₅,₁₆ = 6.908, what is the LOWER limit of the interval?
(16 * 137324.3) / 28.845
(16 * 137324.3) / 6.908
137324.3 / 28.845
137324.3 / 6.908
Question 11 of 40
Quiz ID: q11
Using the values from Q10 (n=17, s²=137324.3, χ²₀.₀₂₅,₁₆=28.845, χ²₀.₉₇₅,₁₆=6.908), calculate the UPPER limit of the 95% CI for the population variance.
76,200
318,000
219,7000
1,370,000
Question 12 of 40
Quiz ID: q12
If you wanted a narrower confidence interval for a mean, which of these actions would achieve that?
Increase the confidence level (e.g., from 95% to 99%).
Decrease the sample size.
Increase the sample size.
The width of the interval is fixed and cannot be changed.
Question 13 of 40
Quiz ID: q13
Everything else being equal, a 99% confidence interval will be __________ a 95% confidence interval.
narrower than
wider than
the same width as
unrelated to
Question 14 of 40
Quiz ID: q14
The breakdown voltage of 10 randomly selected insulators are measured: 62, 58, 64, 55, 69, 61, 59, 67, 60, 63 (in kV). What is the point estimate for the population mean breakdown voltage (μ)?
61.8 kV
62.0 kV
61.0 kV
The sample size is too small to calculate.
Question 15 of 40
Quiz ID: q15
Using the data from Q14, if the sample standard deviation is s = 4.22 kV, what is the standard error of the mean?
4.22 / 10
4.22 / √10
√(4.22 / 10)
4.22² / 10
Question 16 of 40
Quiz ID: q16
For the data in Q14 and Q15 (x̄=61.8, s=4.22, n=10), what is the margin of error for a 95% CI? (Use t₀.₀₂₅,₉ = 2.262)
2.262 * (4.22 / √10)
1.96 * (4.22 / √10)
2.262 * 4.22
1.96 * 4.22
Question 17 of 40
Quiz ID: q17
Calculate the 95% confidence interval for the true mean breakdown voltage using the data from Q14-16 (x̄=61.8, s=4.22, n=10, t₀.₀₂₅,₉=2.262, SE≈1.334).
61.8 ± 3.02 → (58.78, 64.82)
61.8 ± 2.62 → (59.18, 64.42)
61.8 ± 1.33 → (60.47, 63.13)
61.8 ± 8.27 → (53.53, 70.07)
Question 18 of 40
Quiz ID: q18
A quality control inspector finds that 12 out of a random sample of 200 chips are defective. What is the point estimate for the population proportion of defective chips (p)?
0.06
0.12
0.005
0.5
Question 19 of 40
Quiz ID: q19
For the scenario in Q18 (ˆp=0.06, n=200), what is the standard error for this proportion?
√((0.06*0.94)/200)
0.06/√200
√(0.06/200)
0.5/√200
Question 20 of 40
Quiz ID: q20
Calculate the 90% confidence interval for the true proportion of defective chips. (ˆp=0.06, n=200, Z₀.₀₅=1.645). The calculated SE is approximately 0.0168.
0.06 ± 0.028 → (0.032, 0.088)
0.06 ± 0.0168 → (0.0432, 0.0768)
0.06 ± 0.033 → (0.027, 0.093)
0.06 ± 0.001 → (0.059, 0.061)
Question 21 of 40
Quiz ID: q21
You are comparing the strength of two alloys. Sample 1 (n₁=25, x̄₁=80 MPa, s₁=5 MPa). Sample 2 (n₂=30, x̄₂=75 MPa, s₂=6 MPa). What is the point estimate for the difference in mean strength, μ₁ - μ₂?
5 MPa
155 MPa
-5 MPa
1 MPa
Question 22 of 40
Quiz ID: q22
For the data in Q21, what is the standard error for the difference between the means?
√(5²/25 + 6²/30)
(5/25 + 6/30)
√(5/25 + 6/30)
(5 + 6)/√(25 + 30)
Question 23 of 40
Quiz ID: q23
Calculate the standard error from Q22. √(5²/25 + 6²/30) = √(25/25 + 36/30) = √(1 + 1.2) = √2.2. What is the value?
1.483
2.2
1.0
1.2
Question 24 of 40
Quiz ID: q24
For a 95% CI for the difference in means (μ₁ - μ₂) from Q21-23 (Point Estimate=5, SE≈1.483, Z₀.₀₂₅=1.96), what is the margin of error?
1.96 * 1.483 ≈ 2.91
1.645 * 1.483 ≈ 2.44
2.5 * 1.483 ≈ 3.71
5 * 1.483 ≈ 7.415
Question 25 of 40
Quiz ID: q25
What is the 95% confidence interval for the difference in mean strength (μ₁ - μ₂) from the previous questions?
5 ± 2.91 → (2.09, 7.91)
5 ± 1.483 → (3.517, 6.483)
80 ± 2.91 → (77.09, 82.91)
75 ± 2.91 → (72.09, 77.91)
Question 26 of 40
Quiz ID: q26
If a 95% CI for a difference in proportions is (-0.10, 0.05), what is the correct interpretation?
Proportion 1 is definitely larger than Proportion 2.
Proportion 2 is definitely larger than Proportion 1.
There may be no significant difference between the proportions.
The sample sizes were too small.
Question 27 of 40
Quiz ID: q27
The central limit theorem is important for constructing confidence intervals for the mean because it:
Guarantees the sample mean is equal to the population mean.
Ensures the sampling distribution of the mean is approximately normal for large n, even if the population isn't.
Tells us the population standard deviation.
Only applies to small sample sizes.
Question 28 of 40
Quiz ID: q28
When constructing a CI for a mean with a small sample (n < 30) from a non-normal population, what should you do?
Use the Z-interval anyway, the CLT still applies.
Use the t-interval, as it is more robust.
You cannot construct a valid CI. More data is needed.
Use the CI for a proportion instead.
Question 29 of 40
Quiz ID: q29
The margin of error for a population proportion depends on all of the following EXCEPT:
The sample proportion ˆp.
The sample size n.
The confidence level (e.g., 90%, 95%).
The true population proportion p.
Question 30 of 40
Quiz ID: q30
If the sample size is doubled, what happens to the margin of error for a mean?
It is halved.
It is reduced by a factor of 1/√2 (about 0.707).
It is doubled.
It stays the same.
Question 31 of 40
Quiz ID: q31
A 'more confident' interval (e.g., 99% vs. 95%) will be wider. This trade-off is between:
Precision and cost.
Confidence and precision.
Accuracy and bias.
Type I and Type II error.
Question 32 of 40
Quiz ID: q32
In the formula for the CI of a variance, why do we use (n-1) instead of n?
It's a mistake; it should be n.
n-1 makes the interval wider, which is more conservative.
Because we use the sample variance s², which itself uses n-1 in its calculation to be unbiased.
It accounts for the confidence level.
Question 33 of 40
Quiz ID: q33
The Chi-square distribution is:
Symmetric and bell-shaped.
Symmetric but not bell-shaped.
Skewed to the right (positive skew).
Skewed to the left (negative skew).
Question 34 of 40
Quiz ID: q34
For a given sample, which confidence interval would be the widest?
90% CI for the mean
95% CI for the mean
99% CI for the mean
90% CI for the variance
Question 35 of 40
Quiz ID: q35
A process engineer claims the variance of a critical dimension is no more than 0.0010 mm². You calculate a 95% CI for the variance to be (0.0007, 0.0015). What does this say about the claim?
The data supports the claim, as 0.0010 is within the interval.
The data refutes the claim, as the entire interval is above 0.0010.
The data refutes the claim, as the entire interval is below 0.0010.
The data is inconclusive regarding the claim.
Question 36 of 40
Quiz ID: q36
If you incorrectly use a Z-interval instead of a t-interval for a mean with a small sample, what is the most likely consequence?
The interval will be too wide.
The interval will be too narrow.
The confidence level will be accurate.
The point estimate will be wrong.
Question 37 of 40
Quiz ID: q37
The primary difference between a standard deviation and a standard error is:
Standard deviation measures spread in data, standard error measures spread in a statistic.
Standard deviation is for populations, standard error is for samples.
Standard deviation is always larger.
There is no difference; the terms are interchangeable.
Question 38 of 40
Quiz ID: q38
All else equal, if the sample variance (s²) increases, what happens to the width of the CI for the population mean?
It decreases.
It increases.
It stays the same.
It becomes negative.
Question 39 of 40
Quiz ID: q39
What is the key assumption behind using the formula for the standard error of the difference between two proportions?
The two sample sizes must be equal.
The two population proportions must be equal.
The samples must be independent and randomly selected.
The populations must be normally distributed.
Question 40 of 40
Quiz ID: q40
The ultimate purpose of constructing a confidence interval in engineering contexts (like breakdown voltage) is to:
Find the exact value of a population parameter.
Provide a range of plausible values to support decision-making under uncertainty.
Prove a hypothesis definitively.
Calculate a sample statistic.
Quiz Summary
Review your answers before submitting
40
Total Questions
0
Answered
40
Remaining
00:00
Time Spent
Submit Quiz
Back to Questions
Previous
Question 1 of 40
Next
!
Confirm Submission
Cancel
Submit Quiz