Deck 14: Confidence Intervals for Means

Question 1

A random sample of clients at a weight loss center were given a dietary supplement to see if it would promote weight loss.The center reported that the 100 clients lost an average of 48 pounds, and that a 95% confidence interval for the mean weight loss this supplement produced has a margin of error of ±7 pounds.

A)95% of the people who use this supplement will lose between 41 and 55 pounds.
B)The average weight loss of clients who take this supplement will be between 41 and 55 pounds.
C)95% of the clients in the study lost between 41 and 55 pounds.
D)We are 95% sure that the average weight loss among the clients in this study was between 41 and 55 pounds.
E)We are 95% confident that the mean weight loss produced by the supplement in weight loss center clients is between 41 and 55 pounds.

Answer 1

We are 95% confident that the mean weight loss produced by the supplement in weight loss center clients is between 41 and 55 pounds.

Question 2

Answer 2

A

Question 3

Answer 3

B

Question 4

Question 5

Question 6

The amounts (in ounces) of juice in eight randomly selected juice bottles are: $$15.0\quad15 .9\quad15 .8\quad15 .7\quad15 .4\quad15 .2\quad15 .2\quad15 .3$$ Construct a 98% confidence interval for the mean amount of juice in all such bottles.

A)(15.04, 15.84)
B)(15.74, 15.14)
C)(15.14, 15.74)
D)(15.04, 15.74)

Question 7

Question 8

Thirty randomly selected students took the calculus final.If the sample mean was 95 and the standard deviation was 6.4, construct a 99% confidence interval for the mean score of all students.

A)(92.12, 97.88)
B)(91.78, 98.22)
C)(93.01, 98.21)
D)(93.01, 96.99)
E)(91.79, 98.21)

Question 9

Which is true about a 95% confidence interval based on a given sample?
I)The interval contains 95% of the population.
II)Results from 95% of all samples will lie in the interval.
III)The interval is narrower than a 98% confidence interval would be.

A)I only
B)II only
C)III only
D)II and III only

Question 10

The principal randomly selected six students to take an aptitude test.Their scores were: Determine a 90% confidence interval for the mean score for all students.

A)(73.26, 84.07)
B)(84.07, 73.26)
C)(83.97, 83.97)
D)(73.36, 83.97)

Question 11

Question 12

Question 13

Question 14

Using the t-tables, software, or a calculator, estimate the critical value of t for the given
Confidence interval and degrees of freedom: 80% confidence interval with df = 11

A)1.372
B)2.718
C)1.280
D)1.356
E)1.363

Question 15

Using the t-tables, software, or a calculator, estimate the critical value of t for the given confidence interval and degrees of freedom: 90% confidence interval with df = 4.

A)1.645
B)1.533
C)2.353
D)2.132
E)4.604

Question 16

Based on a sample of 30 randomly selected years, a 90% confidence interval for the meanannual precipitation in one city is from 48.7 inches to 51.3 inches.Find the margin of error.

A)0.39 inches
B)0.10 inches
C)2.6 inches
D)1.3 inches
E)There is not enough information to find the margin of error.

Question 17

A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test.Their mean score is 76.2 and their standarddeviation is 21.4.Construct the 95% confidence interval for the mean score of all such subjects.

A)(64.2, 83.2)
B)(64.2, 88.2)
C)(74.6, 77.8)
D)(69.2, 83.2)
E)(67.7, 84.7)

Question 18

A certain population is strongly skewed to the right.We want to estimate its mean, so we will collect a sample.Which should be true if we use a large sample rather than a small one?
I.The distribution of our sample data will be closer to normal.
II.The sampling model of the sample means will be closer to normal.
III.The variability of the sample means will be greater.

A)I only
B)II only
C)III only
D)I and III only
E)II and III only

Question 19

A certain population is bimodal.We want to estimate its mean, so we will collect a sample.
Which should be true if we use a large sample rather than a small one?
I)The distribution of our sample data will be more clearly bimodal.
II)The sampling distribution of the sample means will be approximately normal.
III)The variability of the sample means will be smaller.

A)I only
B)II only
C)III only
D)II and III
E)I, II, and III