TQC1 Probability and Statistics II

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Your Key to Passing TQC1 Probability and Statistics II : Instant Access to Test Practice Questions

Free TQC1 Probability and Statistics II Questions

1. 55. If a Type II error occurs, which of the following is true?
  • A true null hypothesis was rejected
  • A false null hypothesis was not rejected
  • A true null hypothesis was accepted
  • A false null hypothesis was rejected

Explanation

A Type II error occurs when the test fails to reject a false null hypothesis. This means a real effect exists, but the test was not powerful enough to detect it — often due to small sample size or high variability.
2. 19. When a researcher concludes that two variables are related because they move together but fails to account for a hidden third variable, this is an example of:
  • A valid causal inference
  • A sampling error
  • A spurious correlation
  • A regression error

Explanation

A spurious correlation occurs when two variables appear related but are both influenced by another unobserved variable. This leads to a misleading perception of causality, which is why correlation alone cannot prove cause and effect.
3. 81. Which test would be most appropriate to compare two population proportions?
  • Two-sample z-test
  • Paired t-test
  • Chi-square test of independence
  • One-sample t-test

Explanation

A two-sample z-test for proportions determines if the difference between two population proportions is statistically significant. It is commonly used in studies comparing success rates or approval percentages between two groups.
4. 4. When interpreting the slope of a regression line, what does the slope represent?
  • The predicted value when x = 0
  • The change in y for every one-unit increase in x
  • The correlation coefficient
  • The average of all x-values

Explanation

The slope shows how much the dependent variable (y) changes for each one-unit increase in the independent variable (x). A positive slope indicates that y increases with x, while a negative slope means y decreases as x increases.
5. 53. A 95% confidence interval for the population mean is (18.5, 21.5). What is the margin of error?
  • 1.0
  • 1.5
  • 2.0
  • 3.0

Explanation

Margin of error (E) = (Upper limit – Lower limit) ÷ 2 = (21.5 – 18.5) ÷ 2 = 1.5. It represents how far the estimate can reasonably vary from the true population mean given the chosen confidence level.
6. 62. A two-sample t-test yields p = 0.048 at α = 0.05. What conclusion should be made?
  • Reject the null hypothesis
  • Fail to reject the null hypothesis
  • Increase the confidence level
  • Collect more data

Explanation

Since the p-value (0.048) is less than α (0.05), the evidence is sufficient to reject the null hypothesis. This suggests that the means of the two populations are significantly different.
7. 37. Which of the following is a potential issue when interpreting a high correlation?
  • It always implies a causal relationship
  • It may result from a confounding variable
  • It proves that x predicts y
  • It means the data are normally distributed

Explanation

A high correlation does not guarantee causation. The observed relationship may be due to a third, confounding variable influencing both factors. Recognizing this prevents incorrect causal inferences in data interpretation.
8. 2. If the correlation coefficient (r) between two variables is –0.85, what does this indicate?
  • A weak positive relationship
  • A strong negative relationship
  • No relationship
  • A perfect positive relationship

Explanation

The correlation coefficient ranges from –1 to +1. Values close to –1 indicate a strong negative relationship, where one variable increases as the other decreases. A value of –0.85 shows a strong and consistent inverse linear pattern.
9. 67. If a test statistic falls within the nonrejection region, what should the researcher conclude?
  • Reject H₀
  • Fail to reject H₀
  • There is a significant difference
  • The test is invalid

Explanation

If the test statistic lies within the nonrejection region, the data do not provide enough evidence to reject H₀. The observed result is consistent with what would be expected if the null hypothesis were true.
10. 6. In regression analysis, the variable that is being predicted is called the:
  • Independent variable
  • Response variable
  • Control variable
  • Categorical variable

Explanation

The response variable (dependent variable) is the one being predicted or explained by the independent variable. For example, in predicting salary based on years of experience, salary is the response variable, and years of experience is the predictor.

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