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MAT 2001 STATISTICAL REASONING EXAM Q & A WITH RATIONALES 2024.
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MAT 2001 STATISTICAL REASONING EXAM Q & A WITH RATIONALES 2024.
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MAT 2001Statistical Reasoning
COMPLETED EXAM
2024
,1. A researcher wants to test the hypothesis that the mean height of
men in a certain population is 175 cm. He collects a random sample
of 100 men and measures their heights. The sample mean is 173
cm and the sample standard deviation is 10 cm. What is the
appropriate test statistic for this hypothesis test?
A) t = -1.96
B) t = -2
C) z = -1.96
D) z = -2
Answer: B) t = -2
Rationale: Since the population standard deviation is unknown, a t-
test is appropriate. The test statistic is calculated as t = (x̄ - μ) / (s /
√n), where x̄ is the sample mean, μ is the population mean, s is the
sample standard deviation, and n is the sample size. Plugging in the
given values, we get t = (173 - 175) / (10 / √100) = -2.
2. A survey asks 500 people to rate their satisfaction with a new
product on a scale from 1 (very dissatisfied) to 5 (very satisfied). The
results are summarized in the following table:
| Rating | Frequency |
|--------|-----------|
|1 | 50 |
|2 | 75 |
|3 | 150 |
|4 | 125 |
|5 | 100 |
What is the mean rating of the product?
A) 3
B) 3.1
C) 3.2
D) 3.3
, Answer: C) 3.2
Rationale: The mean rating is calculated as the weighted average of
the ratings and their frequencies, i.e., (1*50 + 2*75 + 3*150 + 4*125
+ 5*100) / 500 = = 3.2.
3. A coin is tossed 10 times and the number of heads is recorded.
What is the probability distribution of the number of heads?
A) Binomial with n = 10 and p = 0.5
B) Binomial with n = 0.5 and p = 10
C) Poisson with λ = 10
D) Poisson with λ = 0.5
Answer: A) Binomial with n = 10 and p = 0.5
Rationale: The number of heads follows a binomial distribution with
n equal to the number of trials (10) and p equal to the probability of
success (0.5).
4. A random variable X has a normal distribution with mean μ and
standard deviation σ. What is the probability that X is within one
standard deviation of the mean, i.e., P(μ - σ < X < μ + σ)?
A) 0.3413
B) 0.4772
C) 0.6826
D) 0.9544
Answer: C) 0.6826
Rationale: The probability that X is within one standard deviation of
the mean is equal to the area under the normal curve between μ - σ
and μ + σ, which can be found using a standard normal table or a
calculator. The answer is approximately 0.6826.
5. A confidence interval for a population parameter is calculated
from a sample statistic and its margin of error. What does a 95%
confidence level mean?
A) There is a 95% chance that the population parameter is equal to
the sample statistic.
B) There is a 95% chance that the population parameter is within the
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