Question

In the 2015 AFC Championship​ game, there was a charge that the New England Patriots underinflated their footballs for an advantage. The​ Patriots' opponents during the championship game were the Indianapolis Colts. Measurements of the​ Colts' footballs were taken. The balls should be inflated to between 12.5 and 13.5 pounds per square inch​ (psi). The accompanying data consists of six of the eight measurements on the​ Colts' footballs. Complete parts​ (a) and​ (b) below.

12.3512.35

12.7012.70

12.3012.30

12.7512.75

12.5512.55

12.1512.15

a. Test the hypothesis that the population mean is

less thanless than

12.512.5

psi using a significance level of

0.050.05.

State clearly whether the​ Colts' balls are underinflated or not. Assume the conditions for a hypothesis test are satisfied.

Determine the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

muμequals=12.512.5

Upper H Subscript aHa​:

muμgreater than>12.512.5

B.

Upper H 0H0​:

muμnot equals≠12.512.5

Upper H Subscript aHa​:

muμequals=12.512.5

C.

Upper H 0H0​:

muμless than<12.512.5

Upper H Subscript aHa​:

muμgreater than or equals≥12.512.5

D.

Upper H 0H0​:

muμequals=12.512.5

Upper H Subscript aHa​:

muμless than<12.512.5

E.

Upper H 0H0​:

muμgreater than>12.512.5

Upper H Subscript aHa​:

muμless than or equals≤12.512.5

F.

Upper H 0H0​:

muμequals=12.512.5

Upper H Subscript aHa​:

muμnot equals≠12.512.5

The test statistic is

nothing.

​(Round to two decimal places as​ needed.)

The​ p-value is

nothing.

​(Round to three decimal places as​ needed.)

Interpret the results of the test.

Since the​ p-value is

▼

greater than

less than or equal to

the significance​ level,

▼

do not reject

reject

Upper H 0H0.

There is

▼

insufficient

sufficient

evidence to conclude that the population mean is

less thanless than

12.512.5

psi at a significance level of

0.050.05.

Using only the given​ measurements, it appears that the​ Colts' balls

▼

were not

were

underinflated.

b. Use the data to construct a​ 95% confidence interval for the mean psi for the​ Colts' footballs. How does this confidence interval support your conclusion in part​ (a)?

The

9595​%

confidence interval is

nothing

psi to

nothing

psi.

​(Round to two decimal places as needed. Use ascending​ order.)

The confidence interval

▼

does not support

supports

the conclusion in part​ (a) because the value

12.512.5

▼

is

is not

between the upper and lower bounds of the confidence interval.

Click to select your answer(s).

Answer 1

b)

The confidence interval supports the conclusion in part​ (a) because the value12.5 is between the upper and lower bounds of the confidence interval.