Question

To test

Upper H 0H0​:

muμequals=100

versus

Upper H 1H1​:

muμnot equals≠​100,

a simple random sample size of

nequals=1717

is obtained from a population that is known to be normally distributed. Answer parts​ (a)-(d).

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Click here to view the​ t-Distribution Area in Right Tail.

​(a) If

x overbarxequals=104.4104.4

and

sequals=8.78.7​,

compute the test statistic.

tequals=2.0852.085

​(Round to three decimal places as​ needed.)​(b) If the researcher decides to test this hypothesis at the

alphaαequals=0.01

level of​ significance, determine the critical values.The critical values are

negative 2.921 comma 2.921−2.921,2.921.

​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.)

​(c) Draw a​ t-distribution that depicts the critical​ region(s). Which of the following graphs shows the critical​ region(s) in the​ t-distribution?

A.

A symmetric bell-shaped curve is plotted over a horizontal axis. On the far right side of the graph, a vertical line runs from the axis to the curve. The area under the curve to the right of the vertical line is shaded.

B.

A symmetric bell-shaped curve is plotted over a horizontal axis. Two vertical lines, equidistant from the curve's peak at the center, extend from the axis to the curve on the far left and right sides of the graph. The areas under the curve to the left of the left vertical line and to the right of the right vertical line are shaded.This is the correct answer.

C.

A symmetric bell-shaped curve is plotted over a horizontal axis. On the far left side of the graph, a vertical line runs from the axis to the curve. The area under the curve to the left of the vertical line is shaded.Your answer is not correct.

​(d) Will the researcher reject the null​ hypothesis?

A.

The researcher will reject the null hypothesis since the test statistic is between the critical values.

B.

There is not sufficient evidence for the researcher toThere is not sufficient evidence for the researcher to

reject the null hypothesis since the test statistic

isnbsp between

the critical values.

C.

There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values.

D.

The researcher willThe researcher will

reject the null hypothesis since the test statistic

isnbsp not nbsp not between

the critical values.

Answer 1

Solution :

= 100

= 104.4

n = 17

s = 8.7

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 100

H_a : 100

a) Test statistic = t

= ( - ) / s / n

= (104.4 - 100) /8.7 / 17

= 2.085

p(Z >2.085 ) = 1-P (Z < 2.085 ) = 0.0534

P-value = 0.02534

p=0.0534 ≥ 0.01

b) = 0.01

The critical value for a right-tailed test is t_c​=2.921

c)

B.A symmetric bell-shaped curve is plotted over a horizontal axis. Two vertical lines, equidistant from the curve's peak at the center, extend from the axis to the curve on the far left and right sides of the graph. The areas under the curve to the left of the left vertical line and to the right of the right vertical line are shaded.

d)

C.There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values.