BackWhich Is More Likely? Assume that the fertility rates in Exercise 32 are normally distributed. Are you more likely to randomly select a state with a fertility rate of less than 65 or to randomly select a sample of 15 states in which the mean of the state fertility rates is less than 65? Explain.
"[NW] Oil Change The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is skewed right. However, records indicate that the mean time for an oil change is 11.4 minutes, and the standard deviation for oil-change time is 3.2 minutes.
a. To compute probabilities regarding the sample mean using the normal model, what size sample would be required?"
"Reading Rates The reading speed of second-grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.
d. What effect does increasing the sample size have on the probability? Provide an explanation for this result."
"Upper Leg Length The upper leg length of 20- to 29-year-old males is approximately normal with a mean length of 43.7 cm and a standard deviation of 4.2 cm.
Source: “Anthropometric Reference Data for Children and Adults: U.S. Population, 1999–2002”; Volume 361, July 7, 2005.
e. A random sample of 15 males who are 20–29 years old results in a mean upper leg length of 46 cm. Do you find this result unusual? Why?"
"Answer the following questions for the sampling distribution of the sample mean shown to the right.
c. If the sample size is n = 16, what is the standard deviation of the population from which the sample was drawn?"
"Answer the following questions for the sampling distribution of the sample mean shown to the right.
b. What is the value of σx̄?"
"Answer the following questions for the sampling distribution of the sample mean shown to the right.
a. What is the value of μx̄?"
True or False: To cut the standard error of the mean in half, the sample size must be doubled.
The __________ of the sample mean, x̄, is the probability distribution of all possible values of the random variable x̄ computed from a sample of size n from a population with mean μ and standard deviation σ.
Suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ. The sampling distribution of x̄ has mean μx̄ = _________ and standard deviation σx̄ = ________.
Put the following in order from least to greatest.
- t0.10 with 5 degrees of freedom
- t0.10 with 15 degrees of freedom
- z0.10
[NW]
a. Find the t-value such that the area in the right tail is 0.10 with 25 degrees of freedom.
b. Find the t-value such that the area in the right tail is 0.05 with 30 degrees of freedom.
c. Find the t-value such that the area left of the t-value is 0.01 with 18 degrees of freedom. (Hint: Use symmetry.)
d. Find the critical t-value that corresponds to 90% confidence. Assume 20 degrees of freedom.
The procedure for constructing a t-interval is robust. Explain what this means.
In Problems 23 through 26, indicate whether a confidence interval for a proportion or mean should be constructed to estimate the value of the variable of interest. Justify your response.
A developmental mathematics instructor wishes to estimate the typical amount of time students dedicate to studying mathematics in a week. She asks a random sample of 50 students enrolled in developmental mathematics at her school to report the amount of time spent studying mathematics in the past week.