Ch 4

the weight of a population of individuals is distributed not-normally with mean 182.4 pounds and standard deviation 2.76 pounds. A random sample of 35 individual is measured and the average weight is calculated. What is the sampling distribution of the sample average weight

Shape is normal. Mean is 182.4 pounds. Standard error is 0.47 pounds.

The height of fully grown maple trees is distributed normally with mean 87.5 feet and standard deviation 6.25 feet. A random sample of 12 trees is measured and the average height is calculated. What is the sampling distribution of the sample average height

Shape is normal. Mean is 87.5 feet. Standard error is 1.80 feet

What characteristic of the sampling distribution of the sample average is the Central Limit Theorem concerned with?

Shape of the sample averages.

Please select what is NOT the purpose of the Process of Abstraction

To see how the situation fits into the field of statistics.

Please select one answer in response to the statement: "We can never know the true value of a population mean"

True, because we can never see the entire population to do the calculation.

Why does more data values contain more information

Using more data values in the statistics gives a better idea of all the data values in the population

Is there a definite, specific relationship between the spread of the sample average and the spread of the data

Yes, σαvg=σdata/√n

Why is knowing the value of the population mean important

because it gives one value that is in the middle of all the data values

Why is the sample average important in statistics?

because it is the best sample estimator for the population mean.

a town in Sweden was known to have long-lived residents with a mean life span of 80 years. To find out if this was still true, a sociology researcher looked at several samples of 40 residents that had a standard deviation life span of 8 years. What would be the lowest and the highest life span of the middle 90% these residents?

between 77.9 years and 82.1 years

two most important inferential statistical methods.

confidence intervals and statistical tests

A sampling distribution gives the shape, location, and spread of a column of data values

false

The standard error gives the spread of the column of data values

false

The t-Distribution cannot be used to find the probability of an event

false

the sampling distribution of the sample average has the same shape, location, and spread as does the data values

false

is the spread of the sampling distribution of the sample average wider than the spread of the data values.

no, never wider

To make an important decision in life, we want to know what type of information from statistics

population information

What are the major tools used in the Theorize step

schematic curve and transformation equation

Select the correct equation for the t-Equation.

t=x−μ/(s/√n)

What occurs in the Analyze step

the calculations for the method chosen

Why does the population contain more information than a sample

the population has more data values than a sample

steps used in the process to do statistical inference

theorize, analyze, infer

The sampling distribution of the sample average is important in the science of statistics because it can be used to find the probability of events happening with the sample average.

true

The sampling distribution of the sample average is the shape, location, and spread of all possible sample averages with the same sample size taken from the population

true

Theorize Step

A t-value coming from probability

The Analyze Step

A t-value coming from the sample.

steps in the General Method for Solving Problems in Statistics.

Abstract. Theorize. Analyze. Infer

Why is a bigger sample size better than a smaller sample size

As n gets bigger, the sample average gets closer to the population mean

If knowing any one value in a column of data values, why is knowing the value of the population mean important?

Because in the normal distribution, most of the data values are clustered close to the mean value

Why is the t-Curve wider than the z-Curve

Because the sample standard deviation has a wider spread than the population standard deviation.

When the population standard deviation (σ) is not known, why is the sample standard deviation (s >) used to calculate probability

Because the spread of the sample (s) is the best estimate of the spread of the population (σ).

What type of statistics is used to get population information

Inferential statistics because they infer the population values

What occurs in the Infer step

Inferring a population value from a sample value

What is the shape of the sampling distribution of the sample average for a sample from a not-normally distributed population with a sample size of 35?

Normal, because the average is calculated from more than 30 data values

What is the shape of the sampling distribution of the sample average for a sample from a normally distributed population with a sample size of 25

Normal, because the data has the normal shape.

there is only one possible value for the population standard deviation for a given population, . How many possible values are there for the sample standard deviation taken from this population

There are many, many possible values for the sample standard deviation.

The height of men has an unknown distribution with mean 68.2 inches and standard deviation 2.8 inches. A random sample of 61 men is measured and the average calculated. What is the probability that the average height is greater than 69.2 inches

0.0026

The blood pressure human adults follow a normal distribution with mean 116 millimeters of mercury and standard deviation 9.6 millimeters of mercury. A random sample of 18 human adults is measured and the average calculated. What is the probability that the average blood pressure is less than 110, or greater than 122 millimeters of mercury

0.0080

A fishery graduate student caught 10 fish in the university lake and calculated their average length. The standard deviation length of this sample was 1.18 inches. The population mean length of fish in this lake was 3.6 inches. What is the probability of the sample average being less than 2.7 inches or greater than 4.5 inches?

0.04

a new workout app claims that users could burn 350 calories on average per workout session. A local statistics student questions this claim so she gets 12 of her friends to follow the workout app and calculates the average number of calories burned. The standard deviation of this sample of calories burned was found to be 25 calories. What is the probability that the sample average of her friends is over 363

0.05

A kindergarten teacher had an incoming class of 18 students that seemed to be shorter than usual. She measured these students and calculated an average height of 37 inches and a standard deviation height of 2.6 inches. If the population mean height was known to be 39 inches, what percent of a class of incoming kindergarten students would have a sample average less than 37 inches

0.25%

The blood pressure human adults have an unknown distribution with mean 116 millimeters of mercury and standard deviation 9.6 millimeters of mercury. A random sample of 144 human adults is measured and the average calculated. What is the probability that the average blood pressure is less than 116.8 millimeters of mercury

0.8413

The blood pressure human adults follow a normal distribution with mean 116 millimeters of mercury and standard deviation 9.6 millimeters of mercury. A random sample of 18 human adults is measured and the average calculated. What is the probability that the average blood pressure is between 110 and 122 millimeters of mercury?

0.9920

the score of golfers at a local golf course has an unknown distribution with a mean of 77 strokes and a standard deviation of 7.5 strokes. A random sample of 30 golfers is measured and the average calculated. What percentage of average scores is less than 75

7.21%

What is the first step in using the t-Table?

Choose the correct row for the degrees of freedom.

What type of statistics is used to get sample information

Descriptive statistics because they describe the sample

what is the shape of the t-Distribution

The t-curve is bell shaped, but not normal shaped.

What is the spread of the t-Distribution

The t-distribution has a different spread for every degree of freedom.

What is the location of the t-Distribution

The t-distribution has a mean of zero.

A restaurant chain has a known satisfaction rating of 8.6 units. A local restaurant owner wants to know how his restaurant compares, so he asks 25 customers for their satisfaction ratings and records the average rating. The sample standard deviation of this sample was calculated to be 1.5 units. What average rating would the owner need to have so that less than 25% of his customers disliked his restaurant?

The owner would need an average rating of 8.39 units.