Bluebook SAT Test Inference from Sample Statistics and Margin of Error 10

Question 1

A survey of 400 randomly selected teenagers found that 57% own a smartphone, with a margin of error of ±5 percentage points at 95% confidence.
A researcher claims that a majority (more than 50%) of all teenagers own a smartphone.
Which statement best evaluates this claim?

Accepted Answer

The claim is supported because the entire confidence interval (52% to 62%) is above 50%.

Answer

The claim is not supported because the margin of error is too large to draw conclusions.

Answer

The claim is uncertain because 50% is within one margin of error of the sample proportion.

Answer

The claim is supported because the sample proportion of 57% exceeds 50%.

Question 2

Which of the following actions will NOT change the margin of error in a survey?

Accepted Answer

Changing the city in which the survey is conducted while keeping the same sample size and confidence level

Answer

Increasing the sample size

Answer

Changing the confidence level from 95% to 99%

Answer

Increasing the variability in responses

Question 3

A confidence interval for the mean weight of backpacks in a school district is reported as (14.2 lbs, 17.8 lbs) at 95% confidence. A health official claims the true mean backpack weight is 18 lbs. Which conclusion is most appropriate?

Accepted Answer

The official's claim is not supported because 18 lbs is outside the confidence interval.

Answer

The official's claim is supported because 18 lbs is close to the upper bound.

Answer

The official's claim cannot be evaluated without the sample size.

Answer

The official's claim is supported because the interval includes values near 18 lbs.

Question 4

A random sample of 625 college students estimates that the mean hours of sleep per night is 6.8 hours with a margin of error of ±0.4 hours. What sample size would be needed to reduce the margin of error to ±0.2 hours, assuming the same variability?

Accepted Answer

2,500

Answer

1,250

Answer

1,875

Answer

312

Question 5

A polling firm reports that 46% of likely voters support a candidate, with a 95% confidence interval of (41%, 51%). A campaign manager concludes that the candidate is winning because 46% is the sample proportion. Which statement best evaluates this conclusion?

Accepted Answer

The conclusion is not valid because the confidence interval includes values below 50%.

Answer

The conclusion is valid because 46% is the best estimate of the true proportion.

Answer

The conclusion is valid because the confidence interval is centered near 50%.

Answer

The conclusion is not valid because the sample size is likely too small.

Question 6

A manufacturer tests a random sample of 100 light bulbs and finds a mean lifespan of 1,200 hours with a margin of error of ±40 hours at 95% confidence. A customer claims the true mean lifespan is at least 1,250 hours. Which assessment is most appropriate?

Accepted Answer

The claim is not supported because 1,250 hours is outside the confidence interval.

Answer

The claim is supported because 1,250 hours is only slightly above the upper bound.

Answer

The claim is supported because the sample mean is high enough.

Answer

The claim cannot be assessed without knowing the standard deviation.

Question 7

A researcher computes a 90% confidence interval and a 99% confidence interval from the same dataset. How do these intervals compare?

Accepted Answer

The 99% confidence interval is wider than the 90% confidence interval.

Answer

The 90% confidence interval is wider than the 99% confidence interval.

Answer

Both intervals have the same width because they use the same data.

Answer

The 99% confidence interval is narrower because it is more precise.