stats final

rate = t =

-upside down y -time frame (mins)

Sample evidence can prove that a null hypothesis is true.

false

By how many times does the sample size have to be increased to decrease the margin of error by a factor of one eighth ​?

64

Whether a randomly selected individual has​ blood-type O-negative is a binomial random variable. Assume that its probability will be approximated using the normal distribution. Describe the area under the normal curve that will be computed in order to determine the probability that the number of people with blood type​ O-negative is between 18 and 26​, inclusive.

Between x=17.5 and x =26.5

What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success​ p?

EX = np

True or​ false: To construct a confidence interval about a population variance or standard​ deviation, either the population from which the sample is drawn must be​ normal, or the sample size must be large.

False. To construct a confidence interval about a population variance or standard​ deviation, the sample must come from a normally distributed population.

What is the general​ relationship, if​ any, between the sample size and the margin of​ error?

Increasing the sample size by a factor M results in the margin of error decreasing by a factor of 1/ (sqrt M) .

A simple random sample of size nequals61 is obtained from a population with muequals40 and sigmaequals5. Does the population need to be normally distributed for the sampling distribution of x overbar to be approximately normally​ distributed? Why? What is the sampling distribution of x overbar​? Does the population need to be normally distributed for the sampling distribution of x overbar to be approximately normally​ distributed? Why?

No because the Central Limit Theorem states that regardless of the shape of the underlying​ population, the sampling distribution of x overbar becomes approximately normal as the sample​ size, n, increases.

For the​ following, indicate whether a confidence interval for a proportion or mean should be constructed to estimate the variable of interest. Justify your response. Researchers within an organization asked a random sample of 1016 adults aged 21 years or​ older, "Right​ now, do you think the state of moral values in the country as a whole is getting​ better, or getting​ worse?"

The confidence interval for a ----proportion---- should be constructed because the variable of interest is ------an individual's opinion--- which is a ----qualitative variable----.

The normal curve is symmetric about its​ mean, mu.

The statement is true. The normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ Therefore, the normal curve is symmetric about the​ mean, mu.

Suppose the null hypothesis is rejected. State the conclusion based on the results of the test. Three years​ ago, the mean price of a​ single-family home was ​$243 comma 701. A real estate broker believes that the mean price has decreased since then.

There is sufficient evidence to conclude that the mean price of a​ single-family home has decreased.

When testing a hypothesis using the​ P-value Approach, if the​ P-value is​ large, reject the null hypothesis.

false

An experimental drug is administered to 130 randomly selected​ individuals, with the number of individuals responding favorably recorded. Does the probability experiment represent a binomial​ experiment?

Yes, because the experiment satisfies all the criteria for a binomial experiment.

The notation z Subscript alpha is the​ z-score that the area under the standard normal curve to the right of z Subscript alpha is​ _______.

alpha

when do u reject null hypothesis

if p-value is less than alpha

if the p < sign what tail is it

left

The​ _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted​ _______.

level of confidence, (1-alpha) * 100%

normal density function

not a normal looking curve

In a binomial experiment with n trials and probability of success​ p, -------- the binomial random variable X is approximately normal with ------------- and ------------

np(1-p) greater than or equal to 10 u =np sigma = sqrt (np(1-p)

The standard deviation of the sampling distribution of x overbar​, denoted sigma Subscript x overbar​, is called the​ _____ _____ of the​ _____.

standard error of the mean

if we reject the null hypothesis when the statement in the null hypothesis is​ true, we have made a Type​ _______ error.

type 1 error

Suppose a simple random sample of size n is drawn from a large population with mean mu and standard deviation sigma. The sampling distribution of x overbar has mean mu Subscript x overbar=______ and standard deviation sigma Subscript x =______.

u and sigmax = sigma / sqrt (n)

The points at x= ______ and x= _______ are the inflection points on the normal curve.

x = u-sigma and x = u+sigma