Question

A simple random sample of size

nequals=1515

is drawn from a population that is normally distributed. The sample mean is found to be

x overbarxequals=29.429.4

and the sample standard deviation is found to be

sequals=6.36.3.

Determine if the population mean is different from

2424

at the

alpha equals 0.01α=0.01

level of significance. Complete parts ​(a) through ​(d) below.

​(a) Determine the null and alternative hypotheses.

Upper H 0H0​:

▼

sigmaσ

muμ

pp

▼

not equals≠

less than<

equals=

greater than>

2424

Upper H 1H1​:

▼

sigmaσ

pp

muμ

▼

greater than>

equals=

less than<

not equals≠

2424

​(b) Calculate the​ P-value.

​P-valueequals=nothing

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

​(c) State the conclusion for the test.

A.

RejectReject

Upper H 0H0

because the​ P-value is

greater thangreater than

the

alphaαequals=0.010.01

level of significance.

B.

Do not rejectDo not reject

Upper H 0H0

because the​ P-value is

less thanless than

the

alphaαequals=0.010.01

level of significance.

C.

RejectReject

Upper H 0H0

because the​ P-value is

less thanless than

the

alphaαequals=0.010.01

level of significance.

D.

Do not rejectDo not reject

Upper H 0H0

because the​ P-value is

greater thangreater than

the

alphaαequals=0.010.01

level of significance.

​(d) State the conclusion in context of the problem.

There

▼

is

is not

sufficient evidence at the

alpha equals 0.01α=0.01

level of significance to conclude that the population mean is different from

2424.

Answer 1

Answer)

As the population standard deviation is unknown here we will use t test

Ho : u = 24

Ha : u is not eqaul to 24

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

N = 15

Sample mean = 29.4

S.d = 6.3

Claimed mean = 24

Test statistics t = 3.32

Degrees of freedom js equal to n-1, 14

For df 14 and test statistics of 3.32

P-value from t distribution is = 0.005057

As the obtained p-value (0.0051) is less than 0.01(given significance level)

Reject Ho

There is enough evidence to support the claim.