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Part 2: t-Procedures In this part, we will use t-procedures. t-procedures are both confidence intervals and...

Part 2: t-Procedures

In this part, we will use t-procedures. t-procedures are both confidence intervals and hypothesis tests that

use a t distribution. They are called t-procedures because they rely on a t-test statistic and/or a t-critical

value, so we only need to know the results of a sample in order to perform these procedures for a population

mean.

In Part 2, you will use the data file TempSample00-18.

(THIS IS THE DATA)

YEAR,Month,High Temperature

2000,Jan,45

2000,Jan,48

2001,Jan,49

2003,Jan,62

2003,Jan,53

2004,Jan,42

2004,Jan,47

2005,Jan,40

2005,Jan,47

2006,Jan,48

2006,Jan,47

2007,Jan,51

2007,Jan,34

2007,Jan,47

2009,Jan,50

2011,Jan,35

2012,Jan,44

2013,Jan,38

2013,Jan,53

2013,Jan,42

2014,Jan,58

2014,Jan,47

2014,Jan,44

2015,Jan,52

2016,Jan,44

2017,Jan,49

2018,Jan,54

2000,Feb,48

2001,Feb,47

2004,Feb,47

2007,Feb,51

2008,Feb,51

2008,Feb,55

2011,Feb,45

2014,Feb,37

2014,Feb,54

2014,Feb,58

2015,Feb,54

2017,Feb,52

2017,Feb,44

2017,Feb,45

This includes an SRS of daily temperature highs from January and February from the years 2000-2018

(i.e. "recent" highs). The distribution of "recent" daily high temperatures is approximately Normal.

2.1 Getting Started

2.1.1 Understanding the Set-Up

1) Describe the intended population?

2) Describe the sample?

3) Describe the variable of interest?

4) Describe the parameter of interest (in context)?

5) Describe the statistic of interest (in context)? Give a numerical value along with your description.

Round to two decimal places.

2.1.2 Checking Conditions

1) Check that the conditions for using t-procedures are satisfied. If they are not, discuss whether or not it is reasonable to use t-procedures.

2.2 Confidence Intervals

2.2.1 Motivating Question: Confidence Intervals

In 2.2, we will try to answer the question:

What is the average daily temperature high in Portland, OR for the

months of January and February during 2000-2018?

2.2.2 Confidence Interval

1) What degrees of freedom are needed?

2) What critical value is used to compute a 95% confidence interval?

3) Give the 95% confidence interval. Round to two decimal places.

4) Interpret your 95% confidence interval.

2.2.3 Wrap Up

1) Answer the motivating question in 2.2.1.

2.3 Hypothesis Tests (Tests of Significance)

2.3.1 Motivating Question: Hypothesis Tests

In 2.3, we will try to answer the question:

Is there evidence to suggest that the average daily temperature high in Portland,

OR for the months of January and February during 2000-2018 is different than

the historical average of 48.35◦F?

2.3.2 Hypothesis Test

1) Perform a hypothesis test for α = .01. Be sure to interpret your p-value in context.

2.3.3 Wrap Up

1) Answer the the motivating question in 2.3.1.

2.4 Final Remarks

1) Based on the data found in Part 2, what would you say about the daily high temperature for "recent"

years compared to "historical" years?

Solutions

Expert Solution

orchestra answered 1 year ago
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