The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out t
o see whether this is the case. What conclusion is appropriate in each of the following situations?
(a) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n = 26, t = 2.55, a = 0.01
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n = 26, t = 3.95
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
You may need to use the appropriate table in the Appendix of Tables to answer this question.
(a) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n = 26, t = 2.55, a = 0.01
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n = 26, t = 3.95
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
You may need to use the appropriate table in the Appendix of Tables to answer this question.
1 answer:
Answer:
Option C - Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
Step-by-step explanation:
We are given;
n = 15
t-value = 1.66
Significance level;α = 0.05
So, DF = n - 1 = 15 - 1 = 14
From the one-sample t - table attached, we can see that the p - value of 0.06 at a t-value of 1.66 and a DF of 14
Now, since the P-value is 0.06,it is greater than the significance level of 0.05. Thus we do not reject the null hypothesis. We conclude that there is not sufficient evidence that the true diameter differs from 0.5 in.
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Answer:
Let v(t) be the velocity of the car t hours after 2:00 PM. Then . By the Mean Value Theorem, there is a number c such that
with
. Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly
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Step-by-step explanation:
The Mean Value Theorem says,
Let be a function that satisfies the following hypotheses:
- f is continuous on the closed interval [a, b].
- f is differentiable on the open interval (a, b).
Then there is a number c in (a, b) such that
Note that the Mean Value Theorem doesn’t tell us what c is. It only tells us that there is at least one number c that will satisfy the conclusion of the theorem.
By assumption, the car’s speed is continuous and differentiable everywhere. This means we can apply the Mean Value Theorem.
Let v(t) be the velocity of the car t hours after 2:00 PM. Then and
(note that 20 minutes is
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is
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.
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