Content Quiz Ch 7

In a random sample of 504 judges, it was found that 294 were introverts. (1) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.) (2) Find a 99% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limit

1. p= 294/504= 0.5833 2. intr-z-1prop( c=0.99, x= 294, n= 504) lower= 0.53 upper= 0.64

Assume that the population of x values has an approximately normal distribution. 96 173 128 93 75 94 116 100 85 (1) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.) x = s =

1. x= 106.7 s= 29.4

As the degrees of freedom increase, what distribution does the Student's t distribution become more like? a. standard normal b. binomial c. uniform d. chi-square

a. standard normal

True or false? A larger sample size produces a longer confidence interval for μ. a. True. As the sample size increases, the maximal error increases, resulting in a longer confidence interval. b. False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval. c. True. As the sample size increases, the maximal error decreases, resulting in a longer confidence interval. d. False. As the sample size increases, the maximal error increases, resulting in a shorter confidence interval.

b. False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval.

True or false? The point estimate for the population mean μ of an x distribution is x, computed from a random sample of the x distribution. a. False. The mean of the x distribution does not equal the mean of the x distribution and the standard error of the x distribution decreases as n increases. b. True. The mean of the x distribution equals the mean of the x distribution and the standard error of the x distribution decreases as n increases. c. False. The mean of the x distribution does not equal the mean of the x distribution and the standard error of the x distribution increases as n increases. d. True. The mean of the x distribution equals the mean of the x distribution and the standard error of the x distribution increases as n increases.

b. True. The mean of the x distribution equals the mean of the x distribution and the standard error of the x distribution decreases as n increases.

True or false? If the original x distribution has a relatively small standard deviation, the confidence interval for μ will be relatively short. a. True. As σ decreases, E increases, resulting in a shorter confidence interval. b. False. As σ decreases, E increases, resulting in a longer confidence interval. c. True. As σ decreases, E decreases, resulting in a shorter confidence interval. d. False. As σ decreases, E decreases, resulting in a longer confidence interval.

c. True. As σ decreases, E decreases, resulting in a shorter confidence interval.

True or false? Every random sample of the same size from a given population will produce exactly the same confidence interval for μ. a. False. Different random samples may produce different x values, resulting in the same confidence intervals. b. True. Different random samples will produce the same x values, resulting in the same confidence intervals. c. True. Different random samples may produce different x values, resulting in different confidence intervals. d. False. Different random samples may produce different x values, resulting in different confidence intervals.

d. False. Different random samples may produce different x values, resulting in different confidence intervals.

True or false? Consider a random sample of size n from an x distribution. For such a sample, the margin of error for estimating μ is the magnitude of the difference between x and μ. a. False. By definition, the margin of error is the magnitude of the difference between x and σ. b. False. By definition, the margin of error is the magnitude of the difference between x and μ. c. True. By definition, the margin of error is the magnitude of the difference between x and σ. d. True. By definition, the margin of error is the magnitude of the difference between x and μ.

d. True. By definition, the margin of error is the magnitude of the difference between x and μ.

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken seven blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.87 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error

lower limit: 3.96 upper limit: 6.74 margin of error: 1.39

A random sample of medical files is used to estimate the proportion p of all people who have blood type B. (a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.05 from p? (Round your answer up to the nearest whole number.)

n= .5*.5*(1.44/0.05)^2= 208

In order to use a normal distribution to compute confidence intervals for p, what conditions on np and nq need to be satisfied? np < 5; nq > 5 np > 5; nq < 5 np < 5; nq < 5 np > 5; nq > 5

np > 5; nq > 5

For a binomial experiment with r successes out of n trials, what value do we use as a point estimate for the probability of success p on a single trial?

p= r/n