Question

According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:

Action	% of time
On Time	72
National Aviation System Delay	8
Aircraft arriving late	10
Other (weather and other conditions)	10

When a study was conducted it was found that of the 234 randomly selected flights, 168 were on time, 21 were a National Aviation System Delay, 23 arriving late , 22 were due to weather. Perform a test to see if there is sufficient evidence at αα = 0.10 to see if these differ from the governments statistics.

The correct hypotheses are:

• H0:H0: The sample is a good fit to the Bureau of Transportation Statistics. HA:HA: The sample is not a good fit to the Bureau of Transportation Statistics.(claim)
• H0:H0: The sample is not a good fit to the Bureau of Transportation Statistics. HA:HA: The sample is a good fit to the Bureau of Transportation Statistics.(claim)
• H0:H0: The sample and the Bureau of Transportation Statistics are independent. HA:HA: The sample and the Bureau of Transportation Statistics are dependent.(claim)
• H0:H0: The sample and the Bureau of Transportation Statistics are dependent. HA:HA: The sample and the Bureau of Transportation Statistics are independent.(claim)

The test value is  (round to 3 decimal places)

The p-value is  (round to 3 decimal places)

The correct decision is to

• reject H0H0
• do not reject H0H0

The final conclusion is

• There is enough evidence to reject the claim.
• There is not enough evidence to reject the claim.
• There is enough evidence to support the claim.
• There is not enough evidence to support the claim

Is the length of time of unemployment related to the type of industry? A random sample of unemployed workers from three different work sectors yielded the following data. Perform a hypothesis test at 0.10 level of significance to determine if there is a relationship.

	Less than 5 weeks	5-14 weeks	15-26 weeks
Transportation	86	113	82
Information	53	58	54
Financial	81	113	112

What are the expected numbers? (round to 3 decimal places)

	Less than 5 weeks	5-14 weeks	15-26 weeks
Transportation
Information
Financial

The hypotheses are

H0:H0: The length of unemployment is independent of the type of industry.

HA:HA: The length of unemployment is dependent of the type of industry. (claim)

Since αα = 0.10 the critical value is 7.779

The test value is:  (round to 3 decimal places)

The p-value is  (round to 3 decimal places)

So the decision is to

• do not reject H0H0
• reject H0H0

Thus the final conclusion is

• There is not enough evidence to reject the claim that the length of unemployment is dependent of the type of industry.
• There is enough evidence to support the claim that the length of unemployment is dependent of the type of industry.
• There is enough evidence to reject the claim that the length of unemployment is dependent of the type of industry.
• There is not enough evidence to support the claim that the length of unemployment is dependent of the type of industry.

A student wants to see if the number of times a book has been checked out of the library in the past year and the number of pages in the book are related. She guesses that the number of times a book has been checked out of the library in the past year will be a predictor of the number of pages it has. She randomly sampled 12 books from the library, test her claim at a 0.05 level of significance.

number of times checked out	number of pages
45	290
28	390
16	273
30	274
48	255
36	306
37	300
8	402
34	313
33	344
42	345
8	383

The correlation coefficient:

r= (round to 3 decimal places)

The equation y=a+bx is: (round to 3 decimal places)

y=+ x

The hypotheses are:

H0:ρ=0H0:ρ=0 (no linear relationship)
HA:ρ≠0HA:ρ≠0 (linear relationship) (claim)

Since αα is 0.05 the critical value is -2.228 and 2.228

The test value is:  (round to 3 decimal places)

The p-value is:  (round to 3 decimal places)

The decision is to

• reject H0H0
• do not reject H0H0

Thus the final conclusion sentence is

• There is enough evidence to reject the claim that there is a linear relationship.
• There is not enough evidence to reject the claim that there is a linear relationship.
• There is enough evidence to support the claim that there is a linear relationship.
• There is not enough evidence to support the claim that there is a linear relationship.

Answer 1

1)

H0: The sample is a good fit to the Bureau of Transportation Statistics.

HA: The sample is not a good fit to the Bureau of Transportation Statistics.(claim)

observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
168	0.720	168.48			0.001
21	0.080	18.72			0.278
23	0.100	23.40			0.007
22	0.100	23.40			0.084

chi square test statistic,X² = Σ(O-E)²/E =   0.370

level of significance, α=   0.1              
Degree of freedom=k-1=   4   -   1   =   3
                  
P value =   0.9464   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value >α , Do not reject Ho                  

• There is not enough evidence to support the claim