Question

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Consider the following hypothesis test.

*H*_{0}: *μ* ≥ 40

*H*_{a}: *μ* < 40

A sample of 36 is used. Identify the *p*-value and state
your conclusion for each of the following sample results. Use

*α* = 0.01.

(a)

*x* = 39 and * s* = 5.3

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the *p*-value. (Round your answer to four decimal
places.)

*p*-value =

State your conclusion.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that *μ* < 40.Reject
*H*_{0}. There is insufficient evidence to conclude
that *μ* < 40. Reject
*H*_{0}. There is sufficient evidence to conclude
that *μ* < 40.Do not reject *H*_{0}. There
is insufficient evidence to conclude that *μ* < 40.

(b)

*x* = 38 and * s* = 4.6

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the *p*-value. (Round your answer to four decimal
places.)

*p*-value =

State your conclusion.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that *μ* < 40.Reject
*H*_{0}. There is insufficient evidence to conclude
that *μ* < 40. Reject
*H*_{0}. There is sufficient evidence to conclude
that *μ* < 40.Do not reject *H*_{0}. There
is insufficient evidence to conclude that *μ* < 40.

(c)

*x* = 41 and * s* = 6.0

Find the value of the test statistic.

Find the *p*-value. (Round your answer to four decimal
places.)

*p*-value =

State your conclusion.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that *μ* < 40.Reject
*H*_{0}. There is insufficient evidence to conclude
that *μ* < 40. Reject
*H*_{0}. There is sufficient evidence to conclude
that *μ* < 40.Do not reject *H*_{0}. There
is insufficient evidence to conclude that *μ* < 40.

Answer #1

Null and Alternative hypothesis:

Ho : µ ≥ 40

H1 : µ < 40

n = 36

α = 0.01

(a)

*x* = 39 and * s* = 5.3

Test statistic:

t = (x̅- µ)/(s/√n) = (39 - 40)/(5.3/√36) **=
-1.132**

df = n-1 = 35

p-value = T.DIST(-1.1321, 35, 1) = **0.1326**

State your conclusion.

Do not
reject *H*_{0}. There is insufficient evidence to
conclude that *μ* < 40.

(b)

*x* = 38 and * s* = 4.6

Test statistic:

t = (x̅- µ)/(s/√n) = (38 - 40)/(4.6/√36) =
**-2.609**

df = n-1 = 35

p-value = T.DIST(-2.6087, 35, 1) = **0.0066**

State your conclusion.

Reject
*H*_{0}. There is sufficient evidence to conclude
that *μ* < 40.

(c)

*x* = 41 and * s* = 6.0

Test statistic:

t = (x̅- µ)/(s/√n) = (41 - 40)/(6/√36) =
**1.000**

df = n-1 = 35

p-value = T.DIST(1, 35, 1) = **0.8379**

State your conclusion.

Do not
reject *H*_{0}. There is insufficient evidence to
conclude that *μ* < 40.

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