Exst 2201 Exam 2

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

Population Information

Why does the population contain more information than the sample?

the pouplation has more data vaules than a sample

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.

Select all steps used in the process to do statistical inference.

Theorize
Analyze
Infer

What type of statistics is used to get sample information?

Descriptive statistics because they describe the sample.

What type of statistics is used to get population information?

inferential statistics because they infer the population values.

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.

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.

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 sample average important in statistics?

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

Please select all steps in the General Method for Solving Problems in

Abstract.
Theorize.
Analyze.
Infer.

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

To see how the situation fits into the field of statistics

Please abstract the situation below by matching the symbols with their appropriate numbers.
A 30-year-old veterinarian wanted to know if the puppies born in her clinic weighed less than 0.5 pounds on average. So, she weighed 25 puppies and found a sample average weight of 0.55 pounds.

A.x
B.n
C.μ

A. .55
B. 25
C. 0.5

Please abstract the situation below by matching the symbols with their appropriate numbers.
An engineer was responsible for 5 machines making ball bearings that were supposed to be 1.2 cm in diameter with standard deviation of 0.01 cm. He suspected that one of the machines was making too small ball bearings, so he measured 37 ball bearings from this machine and found an average diameter of 1.15 cm with a standard deviation of 0.015 cm.

A.μ
B.x
C.σ
D.s

A. 1.2 : B. 1.15 : C. 0.01 : D. 0.015

Please abstract the situation below by matching the symbols with their appropriate numbers.
Zillow lists the average home price in our area as $215,816 with a standard deviation of $21,500. To find out if this was still true, a real estate professional collected the data for 58 recently sold homes and found an average of $235,000 with a standard deviation of $23,500.

A.μ
B.x
C.σ
D.s

A: $215,816
B : $235,000
C : $21,500
D : $23,500

What are the major tools used in the Theorize step?

A schematic curve.
A probability table.
A transformation equation.

What occurs in the Analyze step?

The calculations for the method chosen.

What occurs in the Infer step?

Inferring a population value from a sample value.

Please select an appropriate end result for the following two steps of the General Method for Solving Problems in Statistics.

A.
The Theorize Step
B.
The Analyze Step

A. a t-value coming from the probability : B. a t-value coming from the sample

Please select the two most important inferential statistical methods.

Confidence intervals.
Hypothesis tests.

A. μ (mu)

population mean

x

individual data point

σ (sigma)

population standard deviation

s

sample standard deviation

In the process of inference, please select the most appropriate answer to the questions below.

A. What is a confidence interval?

B. What is a sample average?

A: An interval estimate of the population mean.
B: A point estimate of the population mean.

A: An interval estimate of the population mean.
B: A point estimate of the population mean.

A: almost never
B: The confidence level number of times

What value is in the middle of a confidence interval?

The value of the sample average.

What information does the confidence level give?

The proportion of times the confidence interval captures the population mean.

Why does the field of statistics need the method of confidence intervals?

Because we have uncertain data and the population mean cannot be known.

What prior knowledge is the logic of a confidence interval based on?

The sampling distribution of the sample average

Is the interval below a proper denotation of a confidence interval?

No, because the values in the parentheses must go from lowest to highest

In a schematic curve, what area is a confidence interval?

A middle body area.

Please match each summary number with what information probability can add.

A. A population mean (μ)
B. A sample average (x̄).

A: A range of likely values for the sample average.A range of likely values for the population mean.

B: A range of likely values for the population mean.

The confidence limits in a confidence interval are just the x-values of a middle body area in the schematic curve.

true

For a confidence interval, please match each characteristic with its meaning.

A. Its weakness

B. Its strength

A: Every value inside the interval is equally likely to be the population mean.
B: Gives a range of likely, and unlikely, values for the population mean.

What is the correct equation for a confidence interval?

Half of the significance region:Area 1
The confidence region:Area 2
Half of the significance region:Area 3
The critical values:Line 4

What is the correct symbol for the size of the significance region?

alpha

What is the correct equation for the size of the significance region?

alpha = 1 - CL

Every confidence interval contains the value of the population mean.

false

Viewed in terms of probability, a confidence interval situation is just a what?

A middle body area

What is the critical t-value for a 95% confidence interval with 22 data values?

2.08

What is the critical t-value for a 90% confidence interval with 31 data values?

1.697

What is the critical t-value for a 99% confidence interval with 10 data values?

3.250

Please match the following characteristics of a confidence interval with the appropriate answer.

A.Shape

B. Spread

C. Location

shape = the normal shape
spread = the margin of error
location = sample average

In the equation below, what part is the margin of error?

CI/ s/?n

What information does the margin of error give?

half the width of a confidence interval

*For a bigger confidence level, what happens to the width of the confidence interval?

Gets wider, because the middle body area is larger.

With more data values, what happens to the width of the confidence interval?

gets narrower, because the Standard error of the sample average gets smaller

What value is subtracted from the number of data values (n) to get the degrees of freedom for a t-distribution?

1

What is the appropriate situation to use a t-distribution?

When know s, but don't know σ.

A confidence interval is used to infer the sample average.

false

What values are inside a properly made confidence interval?

Likely values for the population mean.

What is the value of the sample average in the confidence interval below?
(96, 118)

107

What is the value of the margin of error in the confidence interval below?
(96, 118)

11

A local college instructor gave a statistics exam to his class of 31 students where the exam scores were normally distributed with an average score of 80 and a standard deviation score of 10. A competing college knew all their students scored 85 on this test. What is the 95% confidence interval to help find out how these local college students did in comparison to the competing college students?

(76.3, 83.7)

A local college instructor gave a statistics exam to his class of 31 students and calculated a 95% confidence interval for the exam scores of (77.1, 82.9). A competing college knew all their students scored an average of 85 on this test. How did the local college do in comparison to the competing college?

Not well, since 85 is higher than the confidence interval.

The height of 14 students in a local college statistics course was measured and found to have an average height of 68 inches and a standard deviation height of 2 inches. What is the 90% confidence interval for the mean height of all students at the college?

(67.0, 68.9)

The height of 14 students in a local college statistics course was measured and found to have a 90% confidence interval of (65.9, 69.9). Is the mean height of all the students at this local college 5 feet 6 inches or higher?

Yes, because 66 inches is inside the confidence interval.

The ages of 21 people in a local elder care home had an average age of 80 years and a standard deviation age of 8 years. What is the 99% confidence interval for the mean age of all people in elder care homes?

(75.0, 85.0)

The ages of 21 people in a local elder care home were measured and a 99% confidence interval of (76.6, 83.4) was calculated. Is the mean age of all people in elder care homes greater than 75 years old?

Yes, because the lower confidence limit is greater than 75.

The population mean must be known to calculate a confidence interval.

false

A fishery graduate student wanted to know the mean length of the perch in a local lake, so she caught 10 perch and measured their length. She found that these perch had an average length of 3.6 inches and a standard deviation length of 1.39 inches. What is the 95% confidence interval for the mean length of the perch in the lake?

(2.61, 4.59)

In 2015 on the National Assessment of Educational Progress (NAEP) science scale\:
15 black students had an average score of 125 and a standard deviation score of 5.81, while
15 hispanic students had an average score of 136 and a standard deviation score of 3.87.

Please make two 98% confidence intervals to see if it is reasonable that students of these two races had the same population mean score

No, it is not reasonable that these two groups have the same mean score because the two confidence intervals do not overlap.

An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He looked up 24 car crashes and found that the average repair cost was $11,000 with a standard deviation cost of $2,500. Please find the middle and spread of a 98% confidence interval for the true mean repair cost.

$11,000 ± $1,275

91 eggs were randomly chosen from a gravid female salmon and individually weighed. The average weight was 0.978 grams with a standard deviation weight of 0.042 grams. Please find the middle and spread of a 90% confidence interval for the weight of all salmon eggs.

0.978 ± 0.007g

61 simple random samples of the local college's student body were collected and the number of people preferring their left hand was recorded. These samples had an average of 16 people preferring their left hand with a standard deviation of 4 people. Find a 95% confidence interval for the true proportion of left-handed people in the local college's student body.

(14.98, 17.02)

Find the population mean age of victims of chain snatching during the last year for a sample of size 35 with an average age of 34.25 years and a standard deviation age of 10 years. Use a 96% confidence level.

(30.64, 37.86)

Click the two reasons that the method of hypothesis testing is needed

1) (50%) To find out how reasonable a chosen value is the population mean.

2) (50%) To find out if the population mean is less than, or greater than, a chosen value.

In hypothesis testing, what does reasonableness mean?

How close a chosen value is to the population mean.

In hypothesis testing, what does less than, or greater than, mean?

The population mean could have a value of -∞ , or +∞

Please match the following inequalities, and equality, to their meaning in a distribution.

1) Less than
-A one-tail to the left situation

2) Greater than
-A one-tail to the right situation

3) Not equal to
-A two-tail situation

Click the two assumptions needed for the method of hypothesis testing.

(50%) The individuals were randomly selected.(50%) The sample average is normally distributed

In hypothesis testing, where does the hypothesized value NOT come from?

From the results of the sample.

In hypothesis testing, how is close and far determined?

By converting the situation from the sample distribution into the z, or t, distribution.

Where does the value of a test statistic come from?

From converting the sample average into a z-score, or t-value.

Why is the method of hypothesis testing called an inferential method of statistics?

Because it gives the best guess (infers) from the sample for the value of the population mean.

How does the method of hypothesis testing make an inference (i.e. draw a conclusion) about a population mean?

By seeing if the test statistic is closer to zero (0), or farther from zero, than the critical value.

Click all choices that are steps in the General Method to solve problems in statistics.

(25%) Step A: Abstract - Relevant information from the question.
(25%) Step 1: Theorize - Probability information from theory.
(25%) Step 2: Analyze - Sample information from the abstraction step.
(25%) Step 3: Infer - Population information from the analyze step.

Click all choices that are steps in Step A: Abstract of the General Method to solve problems in statistics.

(50%) Get descriptive statistics from the sample data values.
(50%) Write a set of two hypotheses about the researcher's question

Click which choice is NOT a descriptive statistic.

to

What information does the null hypothesis express?

The currently believed value of the population mean.

What information does the alternative hypothesis express?

The researcher's believed value of the population mean

The null hypothesis always contains an equal sign.

true

Click all choices that are steps in Step 1: Theorize of the General Method to solve problems in statistics.

(50%) Use the schematic curve to analyze the situation from a statistical point of view.
(50%) Find the appropriate critical value(s) for this situation.

Please match each situation below with the information that goes in the middle of the schematic curve

1) Find probability
The known value of the population mean

2) Find a confidence interval
The value of the sample average

3) Do a hypothesis test
The hypothesized value of the population mean

Please match each region below with the appropriate area under a schematic normal curve.

1) The acceptance region
The body area of the schematic normal curve

2) The rejection region
One, or both, tail area(s) of the schematic normal curv

Click which choice below is NOT an appropriate rejection region.

a middle body area

Please match each alternative hypothesis below with the appropriate statistical situation.

A two-tail situation means the critical value is positive and negative. :
H1:μ≠0

A right-tail situation means the critical value is positive. :
H1:μ>0

A left-tail situation means the critical value is negative. :
H1:μ<0

Click all choices that are steps in Step 2: Analyze of the General Method to solve problems in statistics

(50%) Calculate the test statistic from sample information.
(50%) Find the p-value from the test statistic.

Where does the value of the test statistic come from?

to= x-u/ s root n

Click all choices that are the definition of p-value

The area in one (or two) tail(s) from the value of the test statistic

Click the two conclusions possible in Step 3: Infer of the General Method to solve problems in statistics.

(50%) Do REJECT the null hypothesis.
(50%) Do NOT REJECT the null hypothesis.

What does Reject the Null Hypothesis mean?

That the alternative hypothesis is closer to the truth.

In a hypothesis test, click the possible approaches that can be used to make a conclusion in Step 3: Infer.

(33.3%) The Critical Value approach.
(33.3%) The p-Value approach.
(33.3%) The Confidence Interval approach.

The Confidence Interval approach can only be used in a two-tail situation.

true

In a hypothesis test, what is the size of the Type I error?

alpha

A statistically significant result always means a practically significant result to be followed in practice.

false

Please match the following questions with their answers for the t-equation to convert a sample average into a standardized value

A. What goes in the denominator?

B. What goes in the numerator?

A = The spread of the sample average.

B = The location of the sample average (adjusted for mu).

Please choose the location and spread for the t-equation for a dependent two-sample situation.

The location of the difference column d−0.

The spread of the difference column sd/√η

The location of the sample average(x−μ)

The spread of the sample average s/√η

The location of the difference column d−0.

The spread of the difference column sd/√η

Please choose the location and spread for the t-equation for an independent two-sample situation.

The difference in the two locations (x1−x2)

The two spreads combined together √(s1^2/n1)+(s2^2/n2)

The location of the column of differences (x1−x2)

The two spreads added together (S1/√n1)+(s2/√n2)

The difference in the two locations (x1−x2)

The two spreads combined together √(s1^2/n1)+(s2^2/n2)