Question

QUESTION 22 Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times (in minutes) were obtained. Assume the population of the running times is normally distributed. 150 150 180 170 Test the hypotheses at the 10% level of significance. The p-value is between .50 to 10; accept HO Accept HO because test statistics t = 3 > 2.353 Reject HO because test statistict - 3 > 2.353 The p-value is between .05 to 10; accept HO

Answer 1

Hypothesis :

$H_{0}:\mu =140$

$H_{1}:\mu \neq 140$

Data : 150,150,180,170

Mean=162.5

std dev=15

Test statistics:

$t=\frac{\bar{X}-\mu }{s/\sqrt{n}}$

$t=\frac{162.5-140 }{15/\sqrt{4}}$

$t=\frac{22.5 }{7.5}$

$t=3$

At 10% level of significance and 3 df Critical value =2.533

since t=3 >2.533

Reject H0 t=3 >2.53 There is sufficient evidence at 0.10 to conclude that average running time of movies differ from 140 min

P value :

Excel Sytax

P value =TDIST(3,3,2)

=0.057

P value =0.057 <0.10

P value is between 0.05 to 0.10 reject H0

Reject H0 P value = 0.057 <0.10 There is sufficient evidence at 0.10 to conclude that average running time of movies differ from 140 min

A type II error could not been committed in this hypothesis test since H0 was rejected