For this project you will choose one region and perform a hypothesis test for that region. The following data is for the Northeast: New Jersey

We are looking to answer the following question. Has the average winter temperature for $2022$ been colder than the past $11$ winters?

Our hypothesis is going to be that the average winter temperature has been colder this winter. Test the claim at a $5\%$ level of significance.

Note: We defined winter weather as January, February, and March. For consistency, consider the $$average$$ temperature in Fahrenheit from each January, February, and March from $2011-2021$ for your $$Home State$.$ I have included the average winter temperatures for $5$ states where each state represents the $*5$ regions of the lower Continental U$.$S$.$

Use the following chart to calculate the $($the population average$)$ for the given data set for the Northeast: New Jersey

Year Jan Feb Mar

$2011293643$

$2012384152$

$2013343339$

$2014272937$

$2015292337$

$2016323748$

$2017374139$

$2018324239$

$2019333741$

$2020383946$

$2021333245$

Use the following chart to calculate the x$($average of the sample$)$ for the given data set for the Northeast. New Jersey

Year Jan Feb Mar

$2022293544$

What type of hypothesis test do we run? State the Null and Alternate hypotheses:

Ho : Ha :

Is this a right, left or two$-$tailed test? Identify the rejection region.

Is the critical value a

z or t$?$

Why?

What is the value?

Use technology to find the calculated value of z$-$value or t$-$value or the p$-$value. State these below. Make sure to identify if you use z$-$value, t$-$value, or p$-$value.

Do we reject or not reject the null hypothesis?

To determine, compare p$-$value to the alpha, or the z$/$t$-$score value to the critical value and make your decision accordingly.

Use the following chart to calculate the $($the population average$)$ for the given data set for the Northeast: New Jersey

$\backslash$table$[[$Year$,$Jan,Feb,Mar$],[2011,29,36,43],[2012,38,41,52],[2013,34,33,39],[2014,27,29,37],[2015,29,23,37],[2016,32,37,48],[2017,37,41,39],[2018,32,42,39],[2019,33,37,41],[2020,38,39,46],[2021,33,32,45]]$

Use the following chart to calculate the $\stackrel{}{x}($average of the sample$)$ for the given data set for the Northeast. New Jersey

$\backslash$table$[[$Year$,$Jan,Feb,Mar$],[2022,29,35,44]]$