AP Stats Hypothesis Testing 3 β Questions and Answers
Question 1: A school claims its average SAT score is 1100. A sample of 36 students yields xΜ = 1080 and s = 90. What is the test statistic for a one-sample t-test?
- t = β1.33 (Correct answer)
- t = β2.00
- t = β1.00
- t = β0.22
Correct answer: t = β1.33
t = (1080 β 1100) / (90 / β36) = β20 / 15 β β1.33.
Question 2: Which statement about p-values is correct?
- A p-value is the probability that Hβ is true.
- A p-value is the probability of obtaining results as extreme or more extreme, assuming Hβ is true. (Correct answer)
- A small p-value proves the alternative hypothesis.
- The p-value equals 1 β Ξ±.
Correct answer: A p-value is the probability of obtaining results as extreme or more extreme, assuming Hβ is true.
The p-value measures how likely the observed data (or more extreme) would be if Hβ were true, not the probability that Hβ is true.
Question 3: For a chi-square goodness-of-fit test, the degrees of freedom equal:
- n β 1
- Number of categories β 1 (Correct answer)
- Number of categories Γ 2
- Sample size / 2
Correct answer: Number of categories β 1
Degrees of freedom for a goodness-of-fit test = k β 1, where k is the number of categories.
Question 4: A significance test yields z = 2.45 for a right-tailed test. The p-value is approximately:
- 0.007 (Correct answer)
- 0.014
- 0.993
- 0.071
Correct answer: 0.007
For z = 2.45 in a right-tailed test, p = P(Z > 2.45) β 0.007.
Question 5: Which condition is necessary for a two-sample t-test to be valid?
- Both populations must be exactly normal.
- The two samples must be independent of each other. (Correct answer)
- Both sample sizes must exceed 50.
- Population variances must be known.
Correct answer: The two samples must be independent of each other.
Independence between the two groups is a required condition; normality is only needed if sample sizes are small.
Question 6: A researcher uses Ξ± = 0.05 and obtains p = 0.048. A critic argues the result could be due to chance. Which response best addresses this?
- The result is impossible by chance because p < Ξ±.
- There is about a 4.8% chance of results this extreme if Hβ is true, so we reject Hβ but cannot rule out chance entirely. (Correct answer)
- The result is definitely not due to chance.
- The p-value proves the alternative hypothesis.
Correct answer: There is about a 4.8% chance of results this extreme if Hβ is true, so we reject Hβ but cannot rule out chance entirely.
Statistical significance means the result is unlikely under Hβ but does not eliminate the possibility of a Type I error.
Question 7: In a chi-square test of independence, Hβ states that:
- All cell frequencies are equal.
- The two categorical variables are independent. (Correct answer)
- The two categorical variables are associated.
- The expected counts equal the observed counts.
Correct answer: The two categorical variables are independent.
Hβ for a chi-square test of independence asserts no association β the two variables are independent.
AP Stats Hypothesis Testing 3
A school claims its average SAT score is 1100.
A sample of 36 students yields xΜ = 1080 and s = 90.
What is the test statistic for a one-sample t-test?