STAT EXAM 2

the probability that a continuous random variable assumes a particular value is

0

Confidence coefficien

1-a

In general, we follow three steps when formulating the competing hypotheses.

1. Identify the relevant population parameter of interest 2. Determine whether it is a one- or two-tailed test 3. Include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim.

90%- 95%- 99%-

1.645 1.96 2.576

Confidence level

100(1-a)%

One-tailed tests use

< or > in the alternative.

Suppose the average math SAT score for students enrolled at a local community college is 490.4 with a standard deviation of 63.7. A random sample of 49 students has been selected. The standard error of the mean for this sample is

=63.7/SQRT(49) = 9.1.

According to the IRS, the average refund in the 2011 tax year was $3,109. Assuming that the standard deviation for these refunds was $874, what is the standard error of the sample mean for a random sample of 50 tax returns?

=874/SQRT(50) = $123.60

What is tα/2,dftα⁢/2⁢, df for a 99% confidence interval of the population mean based on a sample of 25 observations?

=T.INV(1-0.01/2,25-1) = 2.797

Which of the following meets the requirements of a cluster sample?

A population can be divided into 50 city blocks. The sample will include residents from two randomly chosen city blocks.

familiar bell-shaped distribution.is also called

Also called Gaussian distribution.

Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 574, 444, 694, 538, 635, 617. Find a 95% confidence interval for the mean sale price in San Luis Obispo County.

Average =AVERAGE(574,444,694,538,635,617) = 583.7 Standard Deviation =STDEV.S(574,444,694,538,635,617) = 86.7241

Two basic methods emerge from inferential statistics.•

Estimation.• Hypothesis testing.

For a given sample size n and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the confidence level 100(1−α)%

FALSE

The standard deviation of X¯ suggests that the variation between observations is smaller than the variation between averages.

FALSE

We draw a random sample of size 36 from the normal population with variance 1.9. If the sample mean is 13.5, what is a 95% confidence interval for the population mean?

Lower Limit =13.5-CONFIDENCE.NORM(0.05,SQRT(1.9),36) = 13.0497. Upper Limit =13.5+CONFIDENCE.NORM(0.05,SQRT(1.9),36) = 13.9503.

What is the purpose of calculating a confidence interval?

To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.

The population is divided up into mutually exclusive and collectively exhaustive groups called

clusters

A major portion of statistics is

concerned with statistical inference

type 2 error

do not reject the null hypothesis when it is false.

Unbiased

expected value of an estimator equals the population parameter.

The normal probability distribution or normal distribution is

familiar bell-shaped distribution.

Under what condition is the finite population correction factor used for computing the standard error of X¯ and P¯ ?

n>0.05N

The lognormal distribution

positively skewed and can not be negative

Credibility of statistical inference depends on the

quality of the sample.

Population mean describes a Population proportion describes a

quantitative variable qualitative

Statistic

random variable whose value depends on the sample.

Type I Error

reject the null hypothesis when it is true.

Hypothesis testing is used to

resolve conflicts between two competing hypothesis on a particular population of interest.

Point estimator:

statistic used to estimate a parameter

Statistical quality control involves

statistical techniques used to develop and maintain a firm's ability to produce high-quality goods and services.

Nonresponse bias

systematic difference in preferences between respondents and nonrespondents.

Social-desirability bias

systematic differences between a group's "socially acceptable" responses and the ultimate choice.

Asymptotic:

tails get closer and closer to the horizontal axis but never touch it.

A graph depicting the normal probability density functionis often referred to as

the normal curve or bell curve.

A control chart is a

tool used to monitor the behavior of a production process.

A continuous random variable is characterized by

uncountable values in an interval.

Confidence intervals have a margin of error that accounts for:

• The standard error of the estimator.• The desired confidence level of the interval.

Two-tailed test uses

≠ in the alternative.

A machine that is programmed to package 1.90 pounds of cereal is being tested for its accuracy in a sample of 45 cereal boxes, the sample mean filling weight is calculated as 1.92 pounds. The population standard deviation is known to be 0.06 pounds. Find the 95% confidence interval for the mean.

Lower Limit =1.92-CONFIDENCE.NORM(0.05,0.06,45) = 1.90 Upper Limit =1.92+CONFIDENCE.NORM(0.05,0.06,45) = 1.94

At an academically challenging high school, the average GPA of a high school senior is known to be normally distributed with a variance of 0.25. A sample of 20 seniors is taken and their average GPA is found to be 2.71. Develop a 90% confidence interval for the population mean GPA.

Lower Limit =2.71-CONFIDENCE.NORM(0.1,SQRT(0.25),20) = 2.5261 Upper Limit =2.71+CONFIDENCE.NORM(0.1,SQRT(0.25),20) = 2.8939

We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confidence interval for the population mean?

Lower Limit =27-CONFIDENCE.NORM(0.05,3.5,36) = 25.8567 Upper Limit =27+CONFIDENCE.NORM(0.05,3.5,36) = 28.1433

Which of the following is the necessary condition for creating confidence intervals for the population mean?

Normality of the estimator

A researcher in campaign finance law wants to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.03 for a 95% confidence interval?

Sample size =(NORM.S.INV(1-0.05/2)/0.03)^2*0.5*(1-0.5) = 1067.0719, rounds up to 1068.

According to the Bureau of Labor Statistics it takes an average of 16 weeks for young workers to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. What is the probability that 20 young workers average less than 15 weeks to find a job?

The appropriate Excel function is =NORM.DIST(15,16,2/SQRT(20),TRUE) = 0.0127

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots.What is the probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLVI?

The appropriate Excel function is =NORM.DIST(170/200,0.9,SQRT(0.9*(1-0.9)/200),TRUE) = 0.0092

Population parameter

a constant, its value may be unknown.

Point estimate

a particular value of the estimator.

A confidence interval, or interval estimate, provides a

a range of values that, with a certain level of confidence, contains the population parameter of interest.

Bias

a sample statistic systematically overestimates or underestimates a population parameter.

Selection bias

a systematic underrepresentation of certain groups in the sample.

Population

all items of interest in a statistical problem.

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 95% of Indianapolis residents wanted the Giants to beat the Patriots.What is the probability that from a sample of 50 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI?

cannot be determined

According to the central limit theorem, the sampling distribution of x−μσ/n√.x-μσ/n. approaches the normal distribution as the sample size

increases

One of the simplest continuous probability distributions

is called the continuous uniform distribution.