NFL Pre-Season Teams in the National Football League (NFL) in the US play four pre-season games each year before the regular season starts.

Question

NFL Pre-Season Teams in the National Football League (NFL) in the US play four pre-season games each year before the regular season starts. Do teams that do well in the pre-season tend to also do well in the regular season? We are interested in whether there is a positive linear association between the number of wins in the pre-season and the number of wins in the regular season for teams in the NFL.

Required:
a. What are the null and alternative hypotheses for this test?
b. The correlation between these two variables for the 32 NFL teams over the 10 year period from 2005 to 2014 was 0.067. Use this sample (with n=320) to calculate the appropriate test statistic and determine the p-value for the test.
c. State the conclusion in context, using a 5% significance level.

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Thanh Hà 4 months 2021-07-25T17:24:54+00:00 1 Answers 1 views 0

Answers ( )

    0
    2021-07-25T17:26:44+00:00

    Answer:

    H0 : ρ = 0

    H1 : ρ ≠ 0

    Test statistic = 1.197

    Pvalue = 0.2335

    There is no correlation between the two variables

    Step-by-step explanation:

    The null and alternative hypothesis :

    H0 : No correlation exist,

    H1 : Correlation exist

    H0 : ρ = 0

    H1 : ρ ≠ 0

    Test statistic, T = r / √(1 – r²) / (n – 2)

    T = 0.067 / √(1 – 0.067²) / (320 – 2)

    T = 0.067 / √(0.995511 / 318)

    T = 0.067 / 0.0559512

    T = 1.197

    The Pvalue obtained from the Rscore, at df = 320 – 2 = 318 is 0.2335

    α = 5% = 0.05

    The Pvalue > α ; we fail to reject the null and conclude that, there is no correlation between the two variables.

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