Proportions and Critical Values

Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month?

A 90% confidence interval for the proportion different p1-p2 was calculated to be (0.247, 0.325). Which of the following conclusions is supported by the interval?

• There is evidence to conclude that p1>p2 because 0.325 is greater than 0.247.

• There is evidence to conclude that p1<p2 because 0.325 is greater than 0.247.

• There is evidence to conclude that p1>p2 because all values in the interval are positive.

• There is evidence to conclude that p1<p2 because all values in the interval are positive.

• There is evidence to conclude that p2>p1 because 0.247 and 0.325 are both greater than 0.05.

What is the t-critical value for an 80% confidence interval with n = 8?

• 1.282

• 1.415

• 1.397

• 0.896

Find the critical value necessary to form a 98% confidence level given that n=10 and s=5.82.

• t*=2.821

• t*=1.65

• t*=5.82

• t*=1.23

If a 90% confidence interval for a population proportion is (0.4, 0.6), what is the sample proportion?

• 0.1

• 0.3

• 0.5

• 0.7

• Not enough information to determine.

Biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 centimeters. The biologists will select a random sample of crabs to measure. Which of the following is the most appropriate method to use for such an estimate?

• one-sample z-interval for a sample proportion

• one-sample z-interval for a population proportion

• one-sample z-interval for a difference between population proportions

• two-sample z-interval for a difference between sample proportions

• two-sample z-interval for a difference between population proportions

What is the t-critical value for a 95% confidence interval with a sample size of 75?

• 1.666

• 1.992

• 1.960

• 1.993

The symbol for the sample proportion is __________.

• Z_c

• p̂

• E

• q

A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000?

• 0.001 < p < 0.005

• 0.566 < p < 0.693

• 0.148 < p < 0.252

• 0.023 < p < 0.045