Central Limit Theorem
According to the law of large numbers, as more observations are added to the sample, the difference between the sample mean and the population mean
Tends to become larger
Is inversely affected by the data added
Remains about the same
Tends to become smaller
Tends to become smaller
True/False: The margin of error represents the distance from the point estimate to the lower and upper bounds of a confidence interval.
True
Find the z-scores associated with 99.5% confidence
±2.807
Which of the following statements is false regarding the t-distribution?
The t distribution is symmetric about zero.
The t distribution has thicker tails than the standard normal distribution.
As the degrees of freedom get smaller, the t-distribution’s spread gets smaller.
The t distribution is bell-shaped
As the sample size grows, it gradually approaches the normal distribution.
As the degrees of freedom get smaller, the t-distribution’s spread gets smaller.
A Type I error occurs when….
A. a null hypothesis is rejected but should not be rejected.
B. a null hypothesis is not rejected but should be rejected.
C. a test statistic is incorrect.
A. a null hypothesis is rejected but should not be rejected.
The amount of money collected by a snack bar at a large university has been recorded daily for the past five years. Records indicate that the mean daily amount collected is $3650 and the standard deviation is $600. The distribution is skewed to the right due to several high volume days (including football game days). Suppose that 100 days were randomly selected from the five years and the average amount collected from those days was recorded. Which of the following describes the sampling distribution of the sample mean?
normally distributed with a mean of $365 and a standard deviation of $60
normally distributed with a mean of $3650 and a standard deviation of $60
skewed to the right with a mean of $3650 and a standard deviation of $600
normally distributed with a mean of $3650 and a standard deviation of $600
normally distributed with a mean of $3650 and a standard deviation of $60
Solve the problem.
Suppose a random sample of n = 66 measurements is selected from a population with mean μ = 65 and standard deviation σ = 12. Find the z-score corresponding to a value of x̄ = 65.6. Round your answer to two decimal places
.41
Use qt() to find the t-value, to two decimal places, for which the area below t is 0.005 with 14 degrees of freedom.
-2.98
In a sample of size 25, in order to compute any sample statistic, how many sample values are free to vary?
25
1
24
50
24
Bottles of water have a label stating that the volume is 12 oz. A consumer group suspects the bottles are under‐filled and plans to conduct a test. A Type I error in this situation would mean
A. The consumer group concludes the bottles have less than 12 oz. when the mean actually is 12 oz.
B. The consumer group does not conclude the bottles have less than 12 oz. when the mean actually is less than 12 oz.
C. The consumer group has evidence that the label is incorrect.
A. The consumer group concludes the bottles have less than 12 oz. when the mean actually is 12 oz.
Professor Whata Guy surveyed a random sample of 420 statistics students. One of the questions was "Will you take another mathematics class?" The results showed that 252 of the students said yes. What is the sample proportion, p^ of students who say they will take another math class?
0.252
0.42
0.6
0.775
0.6
A medication is suspected of increasing the likelihood of conceiving a girl. Of 574 pregnancies where the mother was taking this medication during her pregnancy, 525 of them gave birth to a girl. Construct a 95% confidence interval for the proportion of births that result in a girl when the mother is taking this medication.
Use Z*=1.96
0.892<p<0.937
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 90% confidence interval to estimate the true proportion of students who receive financial aid.
.59 ± .002
.59 ± .004
.59 ± .398
.59 ± .057
.59 ± .057
Find the confidence interval specified. Assume that the population is normally distributed.
A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 206 milligrams with s = 12.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
198.0 to 214.0 milligrams
197.8 to 214.2 milligrams
197.9 to 214.1 milligrams
199.4 to 212.6 milligrams
197.9 to 214.1 milligrams
Suppose the null hypothesis, 𝐻0, is: the blood cultures contain no traces of pathogen 𝑋.
State the Type I and Type II errors.
•Type I error: The researcher thinks the blood cultures do contain traces of pathogen 𝑋, when in fact, they do not.
•Type II error: The researcher thinks the blood cultures do not contain traces of pathogen 𝑋, when in fact, they do.
A national caterer determined that 37% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the caterer's food. If p^ is the sample proportion saying that the food is delicious, what is the standard deviation of the sampling distribution of p^?
0.04
What sample size should be used to estimate a population proportion within 0.045 with 95% confidence?
Use Z*=1.96
475
Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 426 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. If the mean and standard deviation of the sample are x=9.5 hours and s.d.=2.2 hours, find a 99% confidence interval for the true mean number of hours a union member is absent per month. Round to the nearest thousandth.
9.5 ± .274
9.5 ± .185
9.5 ± .013
9.5 ± .106
9.5 ± .274
Find the confidence interval specified. Assume that the population is normally distributed.
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 standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.
64.2 to 88.2
74.6 to 77.8
69.2 to 83.2
67.7 to 84.7
67.7 to 84.7
How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 68 tissues during a cold. Suppose a random sample of 2500 people yielded the following data on the number of tissues used during a cold: Xbar = 55, s = 23. Identify the null and alternative hypothesis for a test to determine if the mean number of tissues used during a cold is less than 68.
H0: μ > 68 vs. Ha: μ ≤ 68
H0: μ = 68 vs. Ha: μ > 68
H0: μ = 68 vs. Ha: μ < 68
H0: μ = 68 vs. Ha: μ ≠ 68
H0: μ = 68 vs. Ha: μ < 68