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Confidence Intervals and Estimation Flashcards

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  1. A 95% confidence interval for the difference in two proportions is (-0.05, 0.13). What can be concluded?

    Answer: There is not convincing evidence of a difference in proportions since 0 is in the interval.

    Since 0 is contained in the interval, the data do not provide convincing evidence of a difference between the two proportions.

  2. Which of the following best describes the effect of increasing sample size on a confidence interval?

    Answer: The interval becomes narrower because the standard error decreases.

    Larger sample size reduces the standard error (SE = σ/√n), which decreases the margin of error and narrows the interval.

  3. A researcher constructs a confidence interval for a mean using a sample that was not randomly selected. The main concern is:

    Answer: Bias — the interval may not capture the true population mean.

    Without random sampling, the sample may be biased and the interval may be systematically off, failing to capture the true parameter.

  4. For a large sample two-proportion z-interval, the pooled standard error is used when:

    Answer: Constructing a confidence interval always uses unpooled standard error; pooling is for hypothesis tests.

    For confidence intervals for p1 − p2, the unpooled standard error is always used; pooling is reserved for significance tests where H0: p1 = p2.

  5. The degrees of freedom for a one-sample t-interval with sample size n is:

    Answer: n − 1

    For a one-sample t-procedure, degrees of freedom = n − 1, reflecting the loss of one degree of freedom when estimating σ with s.

  6. A student calculates a 95% CI for a mean as (55, 65) but realizes they used σ when s should have been used. The corrected interval using t* instead of z* will be:

    Answer: Wider, because t* > z* for the same confidence level.

    The t* critical value is always greater than the z* critical value for the same confidence level and finite df, making the t-interval wider.

  7. In a one-sample z-interval for a proportion, the success-failure condition requires:

    Answer: np̂ ≥ 10 and n(1 − p̂) ≥ 10

    The AP Statistics success-failure condition requires at least 10 expected successes and 10 expected failures to use the normal approximation.