Question

Researchers investigated the physiological changes that accompany laughter. Ninety subjects (18-34 years old) watched film clips designed to evoke laughter. During the laughing period, the researchers measured the heart rate (beats per minute) of each subject, with the following summary results:

x overbarxequals=73.273.2 ,

sequals=55.

It is well known that the mean resting heart rate of adults is

7171

beats per minute. Complete parts a through d below.

a. Set up

Upper H 0H0

and

Upper H Subscript aHa

for testing whether the true mean heart rate during laughter exceeds

7171

beats per minute. Choose the correct answer below.

A.

Upper H 0H0 :

muμequals=7171

Upper H Subscript aHa :

muμnot equals≠7171

B.

Upper H 0H0 :

muμnot equals≠7171

Upper H Subscript aHa :

muμequals=7171

C.

Upper H 0H0 :

muμequals=7171

Upper H Subscript aHa :

muμless than<7171

D.

Upper H 0H0 :

muμequals=7171

Upper H Subscript aHa :

muμgreater than>7171

b. If

alphaαequals=0.010.01 ,

find the rejection region for the test. Choose the correct answer below.

A.

zgreater than>2.5752.575

or

zless than<minus−2.5752.575

B.

zgreater than>2.332.33

C.

zgreater than>2.5752.575

D.

zless than<minus−2.332.33

E.

zless than<minus−2.5752.575

F.

zgreater than>2.332.33

or

zless than<minus−2.332.33

c. Calculate the value of the test statistic.

zequals=nothing

(Round to two decimal places as needed.)

d. Make the appropriate conclusion. Choose the correct answer below.

Answer 1

a. Here claim is that the true mean heart rate during laughter exceeds 71.

D.

Upper H 0:

muμequals=71

Upper Ha :

muμgreater than>71

b. The z-critical value for a right-tailed test, for a significance level of α=0.01 is

zc​=2.33

Graphically

B.

zgreater than>2.33

c. Test statistics is

d. As test statistics is in the rejection region we reject the null hypothesis.

Hence we have sufficient evidence to support the claim that the true mean heart rate during laughter exceeds 71.