Chapter 8
As the sample size increases, the margin of error
decreases.
In a random sample of 144 observations, = .6. The 95% confidence interval for p is
.52 to .68.
A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is
170.2 to 189.8.
or the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is the
normal distribution.
The t value for a 95% confidence interval estimation with 24 degrees of freedom is
2.064.
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the
width of the confidence interval to increase.
The z value for a 97.8% confidence interval estimation is
2.29.
From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is
3.92
In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 61 items is selected. The mean of the sample is determined to be 23. The associated number of degrees of freedom for reading the t value is
60.
A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. If we want to provide a 95% confidence interval for the population mean SAT score, the degrees of freedom for reading the t value is
63
It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is
75
If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be
95
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller.
When the level of confidence decreases, the margin of error
becomes smaller.
An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the
interval estimate.
The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
margin of error.
A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the
normal distribution.
When s is used to estimate σ, the margin of error is computed by using the
t distribution.
In interval estimation, the t distribution is applicable only when
the sample standard deviation is used to estimate the population standard deviation.
In developing an interval estimate, if the population standard deviation is unknown
the sample standard deviation must be used.
