Exam 1 - HW 7-12
Suppose that you calculated the sample size needed to estimate a population mean within a given margin of error when 𝜎 is unknown and the answer came out to n = 30.04. How many items should be sampled?
31
Suppose that you calculated the sample size needed to estimate a population mean within a given margin of error when 𝜎 is known, and the answer came out to n = 32.06. How many items should be sampled?
33
If a study is repeated 100 times and for each study a 95% confidence interval is computed, how many of these confidence intervals are expected to contain the true population parameter?
95
Simply observing a difference between two groups is sufficient evidence to reject the Null Hypothesis of no difference. True or False
False
The shape of the sampling distribution of the sample mean is approximately normal. Which of the following choices justifies that statement? The sample size is greater than or equal to 30. A random sample was taken. The population of all wasted minutes in an 8-hour work day is approximately normally distributed. We have sampled less than 10% of the population.
The sample size is greater than or equal to 30.
A P-value offers a way to measure how surprising our sample is if the Null Hypothesis is true. True or False
True
A confidence interval consists of a range of plausible values for the population parameter we are estimating. True or False
True
Determine whether the following statement is true or false. (Use the Empirical Rule.) The percent of values that fall above the mean in a normal distribution will always be 50%.
True
The Null Hypothesis assumes no change or that there is not a relationship between variables. True or False
True
The notation H0 is used to represent the Null Hypothesis. True or False
True
The standard error of the mean provides a measure of how far a sample mean is expected to deviate from the actual mean of the population. True or False
True
A botanist for a large rose farm is told that the company currently averages 557 thousand dollars in sales annually. The company hires her to work as an outside consultant in order to increase their annual sales revenue. The null hypothesis is H0: 𝜇 = 557. (a) Define the appropriate hypothesis test.
Upper tail test
The local school board wanted to see what the average class sizes were in their district. The board decided to sample elementary, middle, and high schools. Suppose a 99% confidence interval for the population mean is found to be (18, 22). Which of the following options is correct?
We can be 99% confident that the true mean number of students in a class is between 18 and 22.
It is known that the length of time that people wait for a city bus to arrive is right skewed with mean 9 minutes and standard deviation 4 minutes. A sample of 36 wait times is randomly selected. What is the shape of the sampling distribution of the sample wait times? approximately normal uniform left skewed right skewed
approximately normal
A nursery worker would like to study the growth of pine trees at an early stage under 2 conditions—a shaded area near the forest line and an open field. She believes that the pine trees growing near the shady forest line will grow taller in 1 year than the trees in the open field. She plants an abundance of pine trees in both locations. A year later, the nursery worker records 75 measurements of the heights of 1-year-old pine seedlings from each area. The average height of the pines near the forest line was 15.6 cm, and the average height of the pines in the open field was 90.8 cm. Assume for both populations that 𝜎 = 2.5 cm. (a) Is this an example of an experiment or an observational study?
experiment
Which is the last step in finding a confidence interval for a population mean?
interpret the confidence interval
A large pharmaceutical company announces that the mean time for a new medicine to start working is less than 13 minutes. The alternative hypothesis is Ha: 𝜇 < 13. What type of hypothesis test is being described in the statement?
lower tail test
It is known that the lengths of songs played on a radio station follow a normal distribution with mean 3.6 minutes and standard deviation 0.4 minutes. A sample of 25 songs is randomly selected. What is the shape of the sampling distribution of the sample mean length? normal uniform left skewed right skewed
normal
A teacher would like to know the average number of hours each night students spend completing homework. Which term best describes the true mean number of hours each night students spend completing homework?
parameter
Given a population that is normally distributed, find the following. What is the name of a statistic that is calculated from a sample and is used to estimate a population parameter? point estimate sampling distribution margin of error standard error
point estimate
A lawyer believes that the average sentence actually served by criminals prosecuted for armed robbery is 14 years. His administrative assistant believes it is longer. The assistant pulls a sample of 100 records to determine the mean amount of time actually served for that crime. (a) Identify the sample.
the 100 records pulled by the administrative assistant
A nursery worker would like to study the growth of pine trees at an early stage under 2 conditions—a shaded area near the forest line and an open field. She believes that the pine trees growing near the shady forest line will grow taller in 1 year than the trees in the open field. She plants an abundance of pine trees in both locations. A year later, the nursery worker records 75 measurements of the heights of 1-year-old pine seedlings from each area. The average height of the pines near the forest line was 15.6 cm, and the average height of the pines in the open field was 90.8 cm. Assume for both populations that 𝜎 = 2.5 cm. Which of the following is the independent variable in this study? the age of the pine trees the pine trees the location of the pine trees the growth of the pine trees
the location of the pine trees
Determine whether the following statement is true or false. A negative z-score means that a data value is below the mean.
true
