Question

Question 2:

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

You will use the data file TempSample00-18.

(THIS is Temp sample 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.

A.

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.

B.

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.

C.

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.

D.

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

E.

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

Answer 1

Que.A

1. Population: High temperature of all days in the month Jan and Feb of the years 2000-2018.

2. Sample : High temperature on the days in the month of Jan and Feb of the years 2000-2018 which can be selected with SRS from the population.

3. High temperature on days in the month of Jan and Feb (2000 -2018) is the variable of interest.

4. Parameter of interest : Average High temperature on days in the month of Jan and Feb (2000 -2018).

5. Statistic of interest : Average High temperature on days in the month of Jan and Feb (2000 -2018) which are selected in sample.

Que.b

In order to solve this question I used R software.

R codes and output:

> x=scan('clipboard')
Read 41 items

> hist(x)
> t.test(x)

One Sample t-test

data: x
t = 50.177, df = 40, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
45.83254 49.67966
sample estimates:
mean of x
47.7561

Conditions for using t-procedures:

Population from which sample is drawn is normally distributed.

From histogram we see that sample come from normal distribution because shape of the histogram is approximately symmetric.

Que.c

1. Degrees of freedom = 40

2. Critical value = 2.021

3. 95% confidence interval = ( 45.83 , 49.68 )

4. We are 95% confident that average high temperature of the population will lie within the confidence interval

( 45.83 , 49.68 )