MCQs: Confidence Interval, Sample size & Probability

Q1.
In evaluating the effectiveness of the state rehabilitation program, a survey of 49 prisoners (from several thousand prisoners in prison) found that 35 percent were repeat offenders. What is the 90 percent confidence interval for the proportion of repeat offenders amount the prisoners?
A. 0.216, 0.484
B. 0.516, 0.784
C. 0.538, 0.762
D. 0.238, 0.462
E. Cannot be calculated from the information given.

Q2
An accountant wants to estimate the average dollar amount of taxes paid by single people aged 10 to 25. Since the accountant handles a large number of people in that age group, she decides to take a sample. If she believes that the true standard deviation is equal to $1500, how many people should she sample if she wants to be 95% confident that her sample mean will differ from the true mean by no more that + or - $200.
A. 55
B. 153
C. 217
D. 865
E. Cannot be calculated from the information given

Q3.
The daily catch of a small tuna fishing fleet from Ocean Foods Company has averaged 130 tons over the last few years, with a standard deviation 42 tons. The probability that during a sample of 36 fishing days the weight of the daily catch will be greater than 144 tons is
A. 0.3707
B. 0.1293
C. 0.4772
D. 0.0228
E. Cannot be determined unless the weight of the daily catch is normally distributed.

Q4.
The daily catch of a small tuna-fishing fleet from Ocean foods Company has averaged 130 tons over the last few years, with a standard deviation of 42 tons. The probability that during a sample of four (4) fishing days, the weight of the daily catch will be between 109 tons and 151 tons is.
A. 0.3830
B. 0.6170
C. 0.6826
D. 0.8413
E. Cannot be determined unless the weight of the daily catch is normally distributed.

Q5.
If, to avoid a non-representative sample, we divide the population into distinct classes, and sample from each class proportional to its size, we are using:
A. Cluster sampling
B. Systematic sampling
C. Stratified sampling
D. Randomised sampling
E. Non-probability sampling

Q6.
The total area under a continuous probability distribution curve:
A. Will vary depending on the application
B. Will always be exactly 1
C. Will always be between 0 and 1
D. Can never be determined exactly.
E. None of the above.

Q7
The amount of instant coffee that a filling machine puts into "120 grams" jars varies from jar to jar and is normally distributed with a standard deviation of 2 grams. If only 2% of jars are to contain less that 120 grams of coffee, what must be the approximate mean weight of these jars?
A. 115.9g
B. 120.0g
C. 117.9g
D. 122.1g
E. 124.1g

Q8.
A pacer (pencil) manufacturer determines that 3 out of every 10 000 pacers produced are defective. If the pacer manufacturer produces 80 000 pencils, what is the probability that 20 or more will be defective? Use the continuity correction.
A. 0.8212
B. 0.5739
C. 0.6499
D. 0.1788
E. 0.4247

Q9.
Which of the following is a correct statement about the sampling distribution of the sample mean (x- bar)?
A. The mean of the sampling distribution of x- is always equal to the population mean.
B. The standard deviation of the sampling distribution is always equal to the population standard deviation divided by the square root of n.
C. The shape of the sampling distribution is always approximately normal.
D. The finite population correction factor applied to the sampling distribution of x- should only be applied when the sample is less that 5% of the population.
E. None of the above are correct statements.

Q10.
A test was conducted to determine the length of time required for a student to read a specified amount of material. All students were instructed to read at the maximum speed at which they could still comprehend the material. Sixteen students took the test, with the following results (in minutes).
25 18 27 29 20 19 25 24 32 21 24 19 23 28 31 22
Assume reading times are approximately normally distributed.
The point estimates (in minutes) for ( u mean) and ( 0 standard deviation) are respectively:
A. 24.19, 1.08
B. 24.19, 4.19
C. 24.19, 18.70
D. 24.19, 4.32
E. Cannot be determined as n<30

Q11. This question relates to the one above.
A 95% confidence interval for the mean length of time (in minutes) required for all students to read the material is.
A. 21.9 to 26.5
B. 22.1 to 26.3
C. 23.6 to 24.8
D. 23.8 to 28.4
E. 22.3 to 26.1