During recent seasons, Major League Baseball has been criticized for the length

Question

During recent seasons, Major League Baseball has been criticized for the length of its regular season games. A survey reported that the average length of a game is 3.5 hours. To test the survey's claim, a baseball enthusiast obtained a random sample of 17 games and recorded the length of the games (measured in hours) as follows:

2.98   2.38   2.40   3.75    2.70   3.20   2.25   3.27    3.23   2.52   3.17   2.58   3.05    4.46   3.18   3.52   3.79

Define µ.

3.5

true average length of a baseball game (in hours)

sample average length of a baseball game (in hours)

None of the above

QUESTION 10

Refer to Question 9. What is the appropriate null hypothesis?

H0 : µ 3.5

H0 : µ > 3.5

H0 : µ = 3.5

None of the above.

QUESTION 11

Refer to Questions 9 and 10. What is the appropriate alternative hypothesis?

Ha : µ > 3.5

None of the above.

QUESTION 12

Refer to Questions 9, 10 and 11. What is the appropriate test to use for this problem?

z-test

t-test

F-test

Binomial test

QUESTION 13

Refer to Questions 9 - 12. What is the value of the test statistic?

z = -2.924

z = 2.924

t = -2.924

t = 2.924

None of the above.

QUESTION 14

Refer to Questions 9 - 13. What is the p-value for this problem?

0.005

0.010

0.05

0.10

None of the above.

QUESTION 15

Refer to Questions 9 - 14. Based on the p-value, what is the appropriate conclusion?

Since the p-value <0.05, reject H0. Therefore, one cannot conclude the true average length of a baseball game is significantly different from 3.5 hours.

Since the p-value <0.05, reject H0. Therefore, can conclude the true average length of a baseball game is significantly different from 3.5 hours.

Since the p-value not <0.05, do not reject H0. Therefore, one can conclude the true average length of a baseball game is significantly different from 3.5 hours.

Since the p-value not <0.05, do not reject H0. Therefore, one cannot conclude the true average length of a baseball game is significantly different from 3.5 hours.

None of the above.

All questions must be CORRECTLY answered for a thumbs-up.

3.5

true average length of a baseball game (in hours)

sample average length of a baseball game (in hours)

None of the above

Explanation / Answer

Given that,
population mean(u)=3.5
sample mean, x =3.0841
standard deviation, s =0.5864
number (n)=17
null, Ho: =3.5
alternate, H1: !=3.5
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.12
since our test is two-tailed
reject Ho, if to < -2.12 OR if to > 2.12
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =3.0841-3.5/(0.5864/sqrt(17))
to =-2.924
| to | =2.924
critical value
the value of |t | with n-1 = 16 d.f is 2.12
we got |to| =2.924 & | t | =2.12
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -2.9243 ) = 0.0099
hence value of p0.05 > 0.0099,here we reject Ho

ANSWERS
---------------
null, Ho: =3.5
alternate, H1: !=3.5
test statistic: -2.924
critical value: -2.12 , 2.12
decision: reject Ho
p-value: 0.0099

    b.  
Since the p-value <0.05, reject H0. Therefore, can conclude the true average length of a baseball game is significantly different from 3.5 hours.

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