Question

A random sample of

862862

births included

426426

boys. Use a

0.010.01

significance level to test the claim that

50.850.8​%

of newborn babies are boys. Do the results support the belief that

50.850.8​%

of newborn babies are​ boys?

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A.

Upper H 0H0​:

pequals=0.5080.508

Upper H 1H1​:

pless than<0.5080.508

B.

Upper H 0H0​:

pequals=0.5080.508

Upper H 1H1​:

pgreater than>0.5080.508

C.

Upper H 0H0​:

pequals=0.5080.508

Upper H 1H1​:

pnot equals≠0.5080.508

D.

Upper H 0H0​:

pnot equals≠0.5080.508

Upper H 1H1​:

pequals=0.5080.508

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is

nothing.

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

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is

nothing.

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

Identify the conclusion for this hypothesis test.

A.

Fail to rejectFail to reject

Upper H 0H0.

There

isis

sufficient evidence to warrant rejection of the claim that

50.850.8​%

of newborn babies are boys.

B.

Fail to rejectFail to reject

Upper H 0H0.

There

is notis not

sufficient evidence to warrant rejection of the claim that

50.850.8​%

of newborn babies are boys.

C.

RejectReject

Upper H 0H0.

There

is notis not

sufficient evidence to warrant rejection of the claim that

50.850.8​%

of newborn babies are boys.

D.

RejectReject

Upper H 0H0.

There

isis

sufficient evidence to warrant rejection of the claim that

50.850.8​%

of newborn babies are boys.

Do the results support the belief that

50.850.8​%

of newborn babies are​ boys?

A.The results do not support the belief that

50.850.8​%

of newborn babies are boys because there was sufficient evidence to show that the belief is untrue.

B.The results support the belief that

50.850.8​%

of newborn babies are boys because there was sufficient evidence to show that the belief is true.

C.The results do not support the belief that

50.850.8​%

of newborn babies are​ boys; the results merely show that there is not strong evidence against the rate of

50.850.8​%.

D.The results support the belief that

50.850.8​%

of newborn babies are boys because there was no evidence to show that the belief is untrue

Answer 1

Solution :

This is the two tailed test .

A) The null and alternative hypothesis is

c) H₀ : p = 0.508

H_a : p 0.508

= x / n = 426/862 = 0.4942

P₀ = 0.508

1 - P₀ = 1 -0.508 = 0.492

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.4942 - 0.508 / [0.508*(0.492) /862 ]

= -0.81

P(z < -0.81) = 0.2090*2 = 0.418

P-value = 0.418

= 0.05    

0.418 > 0.05

B.

Fail to rejectFail to reject

Upper H 0H0.

There

is not

sufficient evidence to warrant rejection of the claim that

50.8​%

of newborn babies are boys.

C.The results do not support the belief that

50.8​%

of newborn babies are​ boys; the results merely show that there is not strong evidence against the rate of

50.8​%.