Have you ever noticed when watching a National Football Leag

Have you ever noticed, when watching a National Football League (NFL) game, that the players spend a lot of time standing around between plays? The following data were collected from a random sample of 12 NFL games. (See exercise 49 on page 373 of your textbook for a similar problem.)

Minutes standing around between plays

64.73

60.49

69.34

71.22

65.59

71.42

57.16

55.64

71.40

73.62

62.80

67.76

Question 3 A   Test the hypothesis that the average time NFL players spend standing around between plays during a game is 59.69 minutes at =0.1.

Step 1:

H0:      µ         

Ha:      µ          >

Step 2:             =

Step 3:             Fill in the row if the hypothesis is one tailed.

Reject H0 if

Fill in the row if the hypothesis is two tailed. The smaller number must be typed first.

Reject H0 if                                        or

Step 4:             =

Step 5:             H0

Step 6:

Step 7: Fill in the row if the Z table is appropriate.

P-value            =

Fill in the row if the t table is appropriate. The lower boundary must go on the left and the upper boundary on the right.

P-value

Question 3 B   Construct a 99% confidence interval for the population average time NFL players spend standing around between plays during a game.

Lower Endpoint                      Upper Endpoint

Question 3 C   What would the P-value be if this were a lower tail hypothesis test? (Mathematically manipulate the P-value from part A to get your answer.)

Fill in the row if the Z table is appropriate.

P-value            =

Fill in the row if the t table is appropriate. The lower boundary must go on the left and the upper boundary on the right.

(Lower Boundary) P-value (Upper Boundary)

Solution

Given that, when watching a National Football League (NFL) game, that the players spend a lot of time standing around between plays.The following data were collected from a random sample of 12 NFL games.

n = number of NFL games = 12

We want to test the hypothesis that ,average time NFL players spend standing around between plays during a game is 59.69 minutes.

It can be written as symbolically,

H₀ : µ = 59.69 minutes Vs H₁ : µ 59.69 minutes.

Since it is an two sided test.

Sample data is given and population standard deviation is unknown so we use t-statistic here.

t = (xbar - µ) / [s / sqrt(n)]

This t-distribution follows with n-1 degrees of freedom.

xbar = x / n = average of the observations.

s = (x - xbar)^2 / (n-1) = standard deviation of observations.

We can make the table for calculating t-statistics is,

By using EXCEL we can compute the values as,

t-statistic = 3.64999

Given that = 0.1

P-value can be calculated by using the command in EXCEL as :

=tdist(x,degrees of freedom,tails)

=tdist(3.64999,11,2)

P-value = 0.003821

By using P-value we can take a decision that is,

If P-value < then reject H₀  at % level of significance.

and if P-value > then fail to reject H₀ at % level of significance.

So here P-value < reject H₀ at % level of significance.

Conclusion : average time NFL players spend standing around between plays during a game is differ from 59.69 minutes.

Construct a 99% confidence interval for the population average time NFL players spend standing around between plays during a game.

c = confidence level = 0.99

xbar = 65.93083

s = 5.923001

n = 12

99% confidence interval for mean is ,

xbar - E < µ < xbar + E

Where E = t_c * s/sqrt(n)

t_c is the t-critical value = 3.4966

E = 3.4966 * 5.923001 / sqrt(12)

E = 5.9786

Lower limit = xbar - E = 59.9522

Upper limit = xbar + E = 71.9094

The 99% confidence interval for the population average time NFL players spend standing around between plays during a game is (59.9522 , 71.9094).

x	(x-xbar)^2
64.73	1.4420007
60.49	29.602667
69.34	11.622417
71.22	27.975284
65.59	0.1161674
71.42	30.130951
57.16	76.927517
55.64	105.90125
71.4	29.911784
73.62	59.123284
62.8	9.8021174
67.76	3.3458507
791.17	385.90129