Business Stats Test 3
the expression zα denotes the z-score with an area of to its left.
1-a
There were 100 random samples of the same size taken from a population which is known to have a normal distribution with some mean and a known standard deviation. A 95% confidence interval for the population mean was constructed for each of the 100 random samples. If all the conditions are satisfied, what percentage of these confidence intervals would capture the true population mean?
Approximately 95% of them
A simple random sample of 150 adults is obtained and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 4.63. The population standard deviation for red blood cell counts is 0.54. Which of the following is true regarding the distribution of sample means?
Even though the distribution of the population data is not given, the distribution of sample means will be approximately normal because the sample size is large enough according to the Central Limit Theorem.
Nurses wondered if birth weights of babies are going up. They knew that the average birth weight of a baby last year was 7.6 pounds. A random sample of 15 weights of babies at the hospital where the nurses work gave an average birth weight of 7.9 pounds. Nurses felt that the birth weights this year were normally distributed. Which of the following is true about the distribution of sample means?
Even though the sample size is less than 30, the distribution of sample means will be normal because the population data follow a normal distribution.
A statistic is biased if the mean of the sampling distribution is equal to the parameter it is intended to estimate
False
The margin of error is _________ the width of the confidence interval
Half
The larger the sample, the __________ accurate the sample mean will be as an estimate of population mean.
More
The larger the sample, the _______ accurate the sample mean will be as an estimate of the population mean.
More
If x is a good estimator for μ, then we expect the values of x to cluster around μ.
True
In most situations, the true mean and standard deviation are unknown quantities that have to be estimated.
True
The operations manager at the corporate headquarters of a large wood products company wanted to estimate the average time that employees spend at their computers each week. The manager randomly sampled employees and obtained a 99% confidence interval of (17.3 hours/week, 22.5 hours/week). In the context of the problem, which of the following interpretations is correct?
We're 99% confident that the average amount of time spent at their computers among the employees at this company is between 17.3 and 22.5 hours per week.
The expression zα denotes the z-score with an area of _______ to its right.
a
The expression zα/2 denotes the z-score with an area of alpha divided by 2α/2
alpha divided by 2α/2 to its right.
The margin of error is _____________ the width of the confidence interval.
half
The more variable the data, the _______ accurate the sample mean will be as an estimate of the population mean.
less
Days before a presidential election, an article based on a nationwide random sample of registered voters reported the following statistic, "52% (±3%) of registered voters will vote for Robert Smith." What is the "±3%" called?
margin of error.
When the population standard deviation is not known, what is used to estimate it?
the standard deviation of the data from the sample
98% CI: (1-a)= 0.2
z.005= 2.326
99% CI: (1-a)= .01
z.005= 2.575
90% CI: (1 -a) = .10
z.05 = 1.645
95% CI: (1-a)= .05
z0.25= 1.96
