TQC1 Probability and Statistics II
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Free TQC1 Probability and Statistics II Questions
A researcher finds r = 0.02 between time spent watching TV and exam scores. What does this mean?
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There is a strong positive relationship
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There is a weak negative relationship
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There is almost no linear relationship
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There is a strong negative relationship
Explanation
A correlation coefficient of 0.02 is very close to zero, indicating almost no linear relationship between TV time and exam scores. The variables may be unrelated or related in a non-linear way.
If a 95% confidence interval for a population proportion is (0.55, 0.65), what is the point estimate (sample proportion)?
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0.55
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0.60
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0.65
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0.10
Explanation
Which of the following situations illustrates dependent events?
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Flipping a coin twice
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Drawing two marbles from a bag without replacement
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Rolling a die and tossing a coin
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Selecting two cards from two different decks
Explanation
Dependent events occur when one outcome affects another. Drawing two marbles without replacement changes the number of marbles and colors left in the bag, making the second draw dependent on the first.
If a p-value is less than the significance level α, what decision should be made regarding the null hypothesis?
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Fail to reject H₀
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Reject H₀
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Accept H₀
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Retest the hypothesis
Explanation
When the p-value is less than α, the observed results are unlikely under the null hypothesis, providing sufficient evidence to reject H₀. This suggests that the alternative hypothesis (H₁) is supported by the data.
If the correlation coefficient (r) = 0, what does this mean?
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There is a perfect linear relationship
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There is no linear relationship between the variables
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The variables are inversely related
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The slope of the regression line is 1
Explanation
A correlation coefficient of 0 indicates no linear relationship between the variables. However, they may still have a nonlinear association — correlation only measures linear patterns.
A population has a mean of 80 and a standard deviation of 12. What is the standard error of the mean for samples of size 36?
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1.5
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2.0
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2.5
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3.0
Explanation
The standard error of the mean (SE) is calculated as σ / √n = 12 / √36 = 12 / 6 = 2. This measures how much sample means are expected to vary around the population mean when sampling repeatedly.
Which of the following is true of the p-value in a chi-square test?
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It depends on the sample mean and standard deviation
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It measures the strength of evidence against the null hypothesis
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It is always equal to α
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It must be greater than 0.10 to reject the null hypothesis
Explanation
The p-value in a chi-square test measures how likely it is to observe the obtained chi-square value (or more extreme) if the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis.
Which of the following represents the complement of event A?
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A or B
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A and B
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All outcomes not in A
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The intersection of A and B
Explanation
The complement of event A, written as A′, includes all outcomes where A does not occur. Complements help calculate probabilities for “not” events using P(A′) = 1 – P(A).
In hypothesis testing, the null hypothesis (H₀) usually represents:
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The claim being tested or a statement of no effect
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A conclusion that must be true
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A significant difference between groups
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An alternative theory researchers hope to prove
Explanation
The null hypothesis (H₀) is a statement of no effect, no difference, or no relationship. It acts as the default or baseline assumption that statistical tests aim to challenge using evidence from the data.
Which of the following best describes a sampling distribution?
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The distribution of data in the sample itself
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The distribution of sample statistics computed from repeated samples of the same size
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The distribution of population parameters
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The list of all individual observations in a sample
Explanation
A sampling distribution represents the probability distribution of a statistic (like the mean or proportion) obtained from repeated random samples of the same size from a population. It shows how sample means vary around the true population mean and is essential for making inferences about populations.
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