Statistics Chapter 5,6,7

probability distribution requirements

1. There is a numerical random variable x and its values are associated with corresponding probabilities. 2. The sum of all probabilities must be 1. 3. Each probability value must be between 0 and 1 inclusive.

Find the critical value zα/2 that corresponds to the confidence level 80​%.

1.28

Find the critical value zα/2 that corresponds to the given confidence level 82%

1.34

Find the critical value tα/2 corresponding to a​ 95% confidence level.

2.01

Which concept below is NOT a main idea of estimating a population​ proportion? A. The sample proportion is the best point estimate of the population proportion. B. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics. Your answer is correct. C. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion. D. Knowing the sample size necessary to estimate a population proportion is important.

B

Which of the following is NOT an observation about critical​ values? A. The number zα/2 is a critical value that is a z score with the property that it separates an area of α/2 in the right tail of the standard normal distribution. B. A critical value is the area in the​ right-tail region of the standard normal curve. Your answer is correct. C. The number zα/2 is a critical value that corresponds to an area of 1−α/2 to its left. D. A critical value is the number on the borderline separating sample statistics that are likely to occur from those that are unlikely to occur.

B

What does it mean to say that the confidence interval methods for the mean are robust against departures from​ normality? A. The confidence interval methods for the mean are robust against departures from​ normality, meaning they only work with distributions that​ aren't normal. B. The confidence interval methods for the mean are robust against departures from​ normality, meaning they work well with distributions that​ aren't normal, provided that departures from normality are extreme. C. The confidence interval methods for the mean are robust against departures from​ normality, meaning they work well with distributions that​ aren't normal, provided that departures from normality are not too extreme. Your answer is correct. D. The confidence interval methods for the mean are robust against departures from​ normality, meaning they​ don't work well with distributions that​ aren't normal.

C

Which of the following is NOT a conclusion of the Central Limit​ Theorem? A. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size. B. The mean of all sample means is the population mean μ. C. The distribution of the sample data will approach a normal distribution as the sample size increases. D. The distribution of the sample means x ​will, as the sample size​ increases, approach a normal distribution.

C

Which of the following is NOT a property of the sampling distribution of the​ variance? A. The sample variances target the value of the population variance. B. The mean of the sample variances is the population variance. C. The expected value of the sample variance is equal to the population variance. D. The distribution of sample variances tends to be a normal distribution.

D

Which of the following is NOT a property of the sampling distribution of the​ variance? A. The mean of the sample variances is the population variance. B. The sample variances target the value of the population variance. C. The expected value of the sample variance is equal to the population variance. D. The distribution of sample variances tends to be a normal distribution.

D

Which of the following is a biased​ estimator? That​ is, which of the following does not target the population​ parameter? Mean Median Your answer is correct. Proportion Variance

Median

The standard deviation of the distribution of sample means is

S.D/sqrt(n)

Which of the following is NOT needed to determine the minimum sample size required to estimate a population​ proportion? Choose the correct answer below. α Standard Deviation Your answer is correct. zα/2 Margin of Error

Standard Deviation

What does the notation zα ​indicate?

The expression zα denotes the z score with an area of α to its right.

A main goal in statistics is to interpret and understand the meaning of statistical values. The​ _______ can be very helpful in understanding the meaning of the mean and standard deviation.

The range rule of thumb

_____________ is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.

The sampling distribution of a statistic

​_____________ is the distribution of sample​ proportions, with all samples having the same sample size n taken from the same population.

The sampling distribution of the proportion

Finding probabilities associated with distributions that are standard normal distributions is equivalent to​ _______.

finding the area of the shaded region representing that probability.

The​ _______ tells us that for a population with any​ distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

central limit theorem

A​ _______ random variable has infinitely many values associated with measurements.

continuous

A​ _______ random variable has either a finite or a countable number of values.

discrete

The​ _______ of a discrete random variable represents the mean value of the outcomes.

expected value

The expression for calculating the mean of a binomial distribution

np

In the binomial probability​ formula, the variable x represents the​ _______.

number of successes

A​ _______ is a single value used to approximate a population parameter.

point estimate

binomal distribution

probability distribution for which there are just 2 possible outcomes with fixed probabilities that sum to 1.0

A​ _______ variable is a variable that has a single numerical​ value, determined by​ chance, for each outcome of a procedure.

random

The​ _______ is the best point estimate of the population mean.

sample mean

For the binomial​ distribution, what is formula finds the standard​ deviation?

sqrt(npq)

A critical​ value, zα​, denotes the​ _______.

z score with an area of α to its right

Which of the following groups has terms that can be used interchangeably with the​ others? Critical​ Value, Percentage, and Probability Critical​ Value, Probability, and Proportion ​Percentage, Probability, and Proportion Critical​ Value, Percentage, and Proportion

​Percentage, Probability, and Proportion