Question 16 A psychologist has prepared an \"Optimum Test\" that is administered

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Question 16

A psychologist has prepared an "Optimum Test" that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future- the higher the score, the more optimistic the class. The mean for this test is 6. The data for a sample of students are presented below:

             7     12     11    15    7    8    15    9    6

If the researcher suspects that her class will have higher level of optimism than the population, answer the questions below using the .05 level of significance.

2. What is the test statistic?

1.860

-3.50

3.50

-1.860

Question 17

A psychologist has prepared an "Optimum Test" that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future- the higher the score, the more optimistic the class. The mean for this test is 6. The data for a sample of students are presented below:

             7     12     11    15    7    8    15    9    6

If the researcher suspects that her class will have higher level of optimism than the population, answer the questions below using the .05 level of significance.

3. What is the critical value?

1.860

-1.860

3.50

-3.50

Question 18

A psychologist has prepared an "Optimum Test" that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future- the higher the score, the more optimistic the class. The mean for this test is 6. The data for a sample of students are presented below:

             7     12     11    15    7    8    15    9    6

If the researcher suspects that her class will have higher level of optimism than the population, answer the questions below using the .05 level of significance.

4. What decision should be made about the null hypothesis?

Fail to reject the null hypothesis

Reject the alternative hypothesis

There is insufficient evidence to indicate that the alternative hypothesis is true.

Reject the null hypothesis

Question 19

A psychologist has prepared an "Optimum Test" that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future- the higher the score, the more optimistic the class. The mean for this test is 6. The data for a sample of students are presented below:

             7     12     11    15    7    8    15    9    6

If the researcher suspects that her class will have higher level of optimism than the population, answer the questions below using the .05 level of significance.

5. What statistical evidence can you provide for your decision?

because p<

because |t| < |t*|

reject null because |t| > |t*|

|t|>|t*|

Question 20

A psychologist has prepared an "Optimum Test" that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future- the higher the score, the more optimistic the class. The mean for this test is 6. The data for a sample of students are presented below:

             7     12     11    15    7    8    15    9    6

If the researcher suspects that her class will have higher level of optimism than the population, answer the questions below using the .05 level of significance.

6. What final conclusion can be made within the context of this example?

There is insufficient evidence to indicate that the class has higher optimism than the population.

Because we rejected the null, we can conclude that there is sufficient evidence to indicate that the class has a higher level of optimism than the population.

There is sufficient evidence to indicate that the class has lower optimism than the population.

There is sufficient evidence to indicate that the class has higher optimism than the population.

1.860

-3.50

3.50

-1.860

Explanation / Answer

Q6.
Given that,
population mean(u)=6
sample mean, x =10
standard deviation, s =3.4278
number (n)=9
null, Ho: =6
alternate, H1: >6
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.86
since our test is right-tailed
reject Ho, if to > 1.86
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =10-6/(3.4278/sqrt(9))
to =3.501
| to | =3.501
critical value
the value of |t | with n-1 = 8 d.f is 1.86
we got |to| =3.501 & | t | =1.86
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 3.5008 ) = 0.00403
hence value of p0.05 > 0.00403,here we reject Ho
ANSWERS
---------------
null, Ho: =6
alternate, H1: >6
test statistic: 3.501
critical value: 1.86
decision: reject Ho, Reject the null hypothesis
p-value: 0.00403, a. because p<

there is sufficient evidence to indicate that the class has higher optimism than the population.

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