Question

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Consider the following hypothesis test.

H_{0}: μ ≥ 50

H_{a}: μ < 50

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 = 49 and s = 5.2

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 < 50.Reject *H*_{0}.
There is insufficient evidence to conclude that μ <
50. Reject *H*_{0}. There is
sufficient evidence to conclude that μ < 50.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that μ < 50.

(b)

x = 48 and s = 4.5

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 < 50.Reject *H*_{0}.
There is insufficient evidence to conclude that μ <
50. Reject *H*_{0}. There is
sufficient evidence to conclude that μ < 50.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that μ < 50.

(c)

x = 51 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 < 50.Reject *H*_{0}.
There is insufficient evidence to conclude that μ <
50. Reject *H*_{0}. There is
sufficient evidence to conclude that μ < 50.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that μ < 50.

Answer #1

Solution :

= 50

n = 36

This is the two tailed test .

The null and alternative hypothesis is

H0 : ≥ 50

Ha : < 50

a) = 49

s = 5.2

Test statistic = t

= ( - ) / s / n

= (49 - 50) / 5.2/ 36

= -1.154

P (t < -1.154 ) = 0.1282

P-value = 0.1282

= 0.01

p=0.1282 ≥ 0.01

-Do not reject H0. There is insufficient evidence to conclude that μ < 50.

b)

= 48

s = 4.7

Test statistic = t

= ( - ) / s / n

= (48 - 50) / 4.5/ 36

= -2.667

P (t < -2.667 ) = 0.00576

P-value = 0.0058

= 0.01

p=0.0058<0.01

-Reject H0. There is sufficient evidence to conclude that μ < 50.

c)

= 51

s = 6

Test statistic = t

= ( - ) / s / n

= (51- 50) /6/ 36

= 1

P (t<1 ) = 0.8379

P-value = 0.8379

= 0.01

p=0.8379 ≥ 0.01

-Do not reject H0. There is insufficient evidence to conclude that μ < 50.

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