BackA technician wants to estimate the average battery life of a new type of smart phone, so he tests 8 randomly selected phones & records the data below. Assuming battery life has a normal dist, make a 90% conf. int. for the mean battery life.
Does hypnotism result in a different success rate for men and women who are trying to quit smoking? Researchers at Science magazine analyzed studies involving 5600 male and female smokers. Of the 2800 females, 644 quit smoking; of the 2800 males, 840 quit smoking. Construct a 90% confidence interval for the difference in proportion of males and females, pM−pF, and use the interval to judge whether there is a difference in the proportions.
Sample Size Dr. Paul Oswiecmiski wants to estimate the mean serum HDL cholesterol of all 20- to 29-year-old males. How many subjects are needed to estimate the mean serum HDL cholesterol of all 20- to 29-year-old males within 1.5 points with 90% confidence, assuming that s = 12.5 based on earlier studies? Suppose that Dr. Oswiecmiski would prefer 95% confidence. How does the increase in confidence affect the sample size required?
"Simulation: Normal Distribution IQ scores based on the Wechsler Intelligence Scale for Children (WISC) are known to be approximately normally distributed with μ = 100 and σ = 15.
a. Use StatCrunch, Minitab, or some other statistical software to simulate obtaining 100 simple random samples of size n = 5 from this population.
b. Obtain the sample mean and sample standard deviation for each of the 100 samples.
c. Construct 95% t-intervals for each of the 100 samples.
d. How many of the intervals do you expect to include the population mean? How many of the intervals actually include the population mean?"
Age of Death-Row InmatesIn 2002, the mean age of an inmate on death row was 40.7 years, according to data from the U.S. Department of Justice. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 32 death-row inmates and finds that their mean age is 38.9, with a standard deviation of 9.6. Construct a 95% confidence interval about the mean age. What does the interval imply?
What requirements must be satisfied in order to construct a confidence interval about a population mean?
[DATA] Family Size A random sample of 60 married couples who have been married 7 years was asked the number of children they have. The results of the survey are as follows:
Note: x̄ = 2.27, s = 1.22.
b. Compute a 95% confidence interval for the mean number of children of all couples who have been married 7 years. Interpret this interval.
[DATA] Family Size A random sample of 60 married couples who have been married 7 years was asked the number of children they have. The results of the survey are as follows:
Note: x̄ = 2.27, s = 1.22.
c. Compute a 99% confidence interval for the mean number of children of all couples who have been married 7 years. Interpret this interval.
Long Life? In a survey of 35 adult Americans, it was found that the mean age (in years) that people would like to live to is 87.9 with a standard deviation of 15.5. An analysis of the raw data indicates the distribution is skewed left.
b. Construct and interpret a 95% confidence interval for the mean.
In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.
c = 0.99, n = 10