1. True or false? The value
z
c
is a value from the standard normal distribution such thatP(−z
c
z z
c
) =c.
True. By definition, critical valueszc
are such that 100c% of the area under the standard normal curve falls in the tails, to the left of −z
c
and to the right ofzc
.
False. By definition, critical valueszc
are such that 100c% of the area under the standard normal curve falls between −z
c
andzc
.
True. By definition, critical valueszc
are such that 100c% of the area under the standard normal curve falls between −z
c
andzc
.
False. By definition, critical valueszc
are such that 100c% of the area under the standard normal curve falls in the tails, to the left of −z
c
and to the right ofzc
.
2. True or false? The point estimate for the population mean μ of anx distribution is , computed from a random sample of thex distribution.
True. The mean of the distribution equals the mean of thex distribution and the standard error of the distribution decreases asn increases.
False. The mean of the distribution does not equal the mean of thex distribution and the standard error of the distribution decreases asn increases.
True. The mean of the distribution equals the mean of thex distribution and the standard error of the distribution increases asn increases.
False. The mean of the distribution does not equal the mean of thex
distribution and the standard error of the distribution increases as
n increases.
3. Sam computed a 90% confidence interval for μ from a specific random sample of sizen. He claims that at the 90% confidence level, his confidence interval contains μ. Is this claim correct? Explain.
Yes. 90% of all confidence intervals will contain μ.
No. The probability that this interval contains μ is either 0 or 1.
No. The proportion of all confidence intervals based on random samples of sizen that contain μ is 0.10.
Yes. The proportion of all confidence intervals based on random samples of sizen that contain μ is 0.90.