Business Stats Test 3

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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


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