Question

Part 1: z-Procedures In this part, we will use z-procedures. z-procedures are both confidence intervals and hypothesis tests that use a Normal distribution. They are called z-procedures because they rely on a z-test statistic and/or a z-critical value. So far, we can use z-procedures for a population mean knowing the population standard deviation. In Part 1, you will use the data file TempSample00-18.

(THIS IS 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

Part 1: z-Procedures

1.1 Getting Started

1.1.1 Understanding the Set-Up

1) Describe the intended population?

The intended population is the months of January and February

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.

1.1.2 Checking Conditions

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

1.2 Confidence Intervals

1.2.1 Motivating Question: Confidence Intervals

In 1.2, 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?

1.2.2 Confidence Interval

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

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

3) Interpret your 95% confidence interval

1.2.3 Wrap Up

1) Answer the motivating question in 1.2.1.

1.3 Hypothesis Tests (Tests of Significance)

1.3.1 Motivating Question: Hypothesis Tests

In 1.3, 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?

1.3.2 Hypothesis Test

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

1.3.3 Wrap Up

1) Answer the the motivating question in 1.3.1.

1.4 Final Remarks

1) Based on your work in Part 1, what would you say about the daily high temperature for “recent” years compared to “historical” years?

Answer 1