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tatuchka [14]
2 years ago
8

A researcher would like to investigate whether or not there is a difference in IQ between Psychology and History majors. She gat

hers 16 students (8 whose major is Psychology, and 8 whose major is history) and has them all take an IQ test to test this hypothesis using an alpha level of .01. Below are the data: Psych History
110 90 120 98 100 100 90110 124 100 102 120 110 110 123 120
a. What is the appropriate test?
b. State the null hypothesis:
c. State the alternative hypothesis:
d. Find the critical value:
e. Calculate the obtained statistic:
f. Make a decision:
g. What does your decision mean?
Mathematics
1 answer:
Over [174]2 years ago
7 0

Answer:

Paired t test

H0 : μd = 0

H1 : μd > 0

Critical value = 3.499

Test statistic = 2.230

Reject H0 if test statistic > Critical value

Kindly check explanation.

Step-by-step explanation:

Given the data :

110 90 120 98 100 100 90 110

124 100 102 120 110 110 123 120

The hypothesis :

H0 : μd = 0

H1 : μd > 0

Tcritical value, df = n - 1 = 8 - 1 = 7

Tcritical(0.01, 7) = 3.499

The difference, d = (-14,-10,18,-22,-10,-10,-33,-10)

The test statistic :

Xdbar / Sd/√n

The mean difference, Xdbar = Σx / n = - 11.375

The standard deviation of difference, Sd = 14.431

The test statistic :

-11.375 / (14.431/√8) ;

-11.375 / 5.102

= 2.230

Decison :

Reject H0 if test statistic > Critical value

Since ; 2.230 <3.499 ;

We fail to reject the null

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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis
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In the question, we are looking for the equations of the circle having a diameter of 12 units and a center lying on y-axis.

The standard form of the equation of a circle is (x - h)² + (y - k)² + r², where (h, k) is the center of the circle, and r is its radius.

A circle having a diameter of 12 units, will have a radius of 12/2 = 6 units. Thus, r = 6.

A circle having the center on the y-axis will have a center as (0, k) as all points on the y-axis have x-coordinate 0.

Thus, the equation of the circle, with a diameter of 12 units and the center lying on the y-axis takes the form:

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From the given options, the equations <u>x² + (y – 3)² = 36</u>, and <u>x² + (y + 8)² = 36</u>, are of this form.

Thus, the equations representing the circle having a diameter of 12 units and a center lying on y-axis are <u>x² + (y – 3)² = 36</u>, and <u>x² + (y + 8)² = 36</u>, making <u>options 1, and 5</u> the two choices.

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The provided question is incomplete. The complete question is:

"Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.

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  2. x² + (y – 5)² = 6
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