BSTAT Exam 2

A telephone company wants to estimate, with 95% confidence, the mean number of minutes people in a city spend talking long distance. From past records, the standard deviation is 12 minutes. What is the minimum sample size required if the desired bound on error does not exceed 5 minutes? Assume the length of a call is normally distributed.

23

Let X be normally distributed with mean µ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736.

29.70

finite population correction factor

A factor used to adjust the standard error of the mean or proportion when the proportion of sample size to population size n/N is greater than 5%

The t statistic is used to estimate the difference between two population proportions.

False

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. Which of the following hypotheses is relevant to this claim?

H0: p1 - p2 ≤ 0, HA: p1 - p2 > 0

Which of the following pairs of hypotheses are used to test if the mean of the first population is greater than the mean of the second population, using independent random sampling?

H0: µ1 - µ2 ≤ 0, HA: µ1 - µ2 > 0

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X = 15) related to P(X < 16)?

P(X < 16) is greater than P(X = 15)

Estimate

Particular value of the estimator

stratified random sampling

Population divided into subgroups (strata) and random samples taken from each strata

The most effective way to deal with no response bias is to:

Reduse nonresponse rates

T/F: If we were to sample from a given population, the avg value of the sample mean will equal the avg value of the population mean

True

T/F: If we were to sample repeatedly from a given population, the avg value of sample mean would equal the avg value of the population mean

True

We use the difference between the sample proportions p-bar1 - p-bar2 as the point estimator of the difference between two population proportions p1-p2.

True

Social Durability Bias

Voters provide incorrect answers to survey because they think that others will look unfavorably on their choices

We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 95% confidence interval for the population mean?

[11.5592, 13.4408]

Simple Random Sample (SRS)

a sample in which each set of n elements in the population has an equal chance of selection

Estimator

a statistic used to estimate a parameter

Detection Approach

a statistical quality control technique that determines at which point the production process does not conform to specifications

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. At the 5% significance level, the decision is to ___________.

do not reject Ho; we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is E = 1.4? The population standard deviation is known to be 10.75.

n=160

If the p-value for a hypothesis test is 0.127 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________________.

not reject the null hypothesis

A recent report claimed that Americans are retiring later in life (U.S. News & World Report, August 17). An economist wishes to determine if the mean retirement age has increased from 62. To conduct the relevant test, she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t37 = 1.92. With α = 0.05, she

rejects the null hypothesis and concludes that the mean retirement age has increased

The hypothesis test H0:p1 - p2 ≤ d0; HA: p1 - p2 > d0 is a left-tailed test.

False

A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X-bar = $50.50 and S2 = 400. Construct a 90% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution.

$50.50 ± $9.09

Advantages to stratified

-Guarantees that the population subdivisions of interested and represented -Estimates of parameters have greater precision

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car.

0.0000

Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power?

0.0478

A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is less than 0.55 is ______.

0.1537

chance variation

Caused by a number of randomly occurring events that are part of the production process

cluster sampling

Divide the population area into sections (or clusters). Then randomly select some of those clusters. Now choose all members from selected clusters. Cheaper, less precision

A 99% confidence interval for the population mean yields the following results: [-3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

Do not reject Ho; we cannot conclude that the mean differs from zero.

A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µ1and µ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Which of the following is the appropriate conclusion at the 5% significance level?

Fail to reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.

For a given confidence level and sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.

False

If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of X1-X2 is approximately normal only if the sum of the sample observations is sufficiently large—that is, when n1+n2 is >/= 30

False

In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A stratified sample includes randomly selected clusters from each stratum, which are proportional to the stratum's size.

False

A ________ is a numerical quantity not computed from the data of a sample and is the size of the critical region used in reaching a decision on whether or not to reject the null hypothesis.

Signifigance level

Statistical Quality Control (SQC)

Techniques used to develop and maintain the ability to produce high quality goods and services

expected value

The mean of a probability distribution.

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 5% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

We cannot conclude that the mean differs or does not differ from zero.

Sampling from a Normal Population

Xbar is normally distributed if population X from which the sample is drawn is normally distributed

Calcium is an essential nutrient for strong bones and for controlling blood pressure and heart beat. Because most of the body's calcium is stored in bones and teeth, the body withdraws the calcium it needs from the bones. Over time, if more calcium is taken out of the bones than is put in, the result may be thin, weak bones. This is especially important for women who are often recommended a calcium supplement. A consumer group activist assumes that calcium content in two popular supplements are normally distributed with the same unknown population variance, and uses the following information obtained under independent sampling:

[-31.5886, -0.4114]

A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim?

t15 = -3.00

Acceptance Sampling

the application of statistical techniques to determine whether a quantity of material should be accepted or rejected based on the inspection or test of a sample

standard error

the standard deviation of a sampling distribution

Central Limit Theorem

the sum or mean of a large number of independent observations made from the same underlying distribution is approximately normally distributed

assignable variation

variation in a production process that can be traced to specific causes to be identified and eliminated

A 99% confidence interval estimate can be interpreted to mean that

we have 99% confidence that we have selected a sample whose interval includes the population mean.