You may need to use the appropriate appendix table or technology to answer this question. Consider the following hypothesis test. H0: ? ≤ 50 Ha: ? > 50 A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use ? = 0.05. (Round your answers to two decimal places.) (a) x = 52.3 Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.) test statistic≤test statistic≥ State your conclusion. Reject H0. There is insufficient evidence to conclude that ? > 50.Reject H0. There is sufficient evidence to conclude that ? > 50. Do not reject H0. There is insufficient evidence to conclude that ? > 50.Do not reject H0. There is sufficient evidence to conclude that ? > 50. (b) x = 51 Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.) test statistic≤test statistic≥ State your conclusion. Reject H0. There is insufficient evidence to conclude that ? > 50.Reject H0. There is sufficient evidence to conclude that ? > 50. Do not reject H0. There is insufficient evidence to conclude that ? > 50.Do not reject H0. There is sufficient evidence to conclude that ? > 50. (c) x = 51.9 Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.) test statistic≤test statistic≥ State your conclusion. Reject H0. There is insufficient evidence to conclude that ? > 50.Reject H0. There is sufficient evidence to conclude that ? > 50. Do not reject H0. There is insufficient evidence to conclude that ? > 50.Do not reject H0. There is sufficient evidence to conclude that ? > 50.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

You may need to use the appropriate appendix table or technology to answer this question.

Consider the following hypothesis test.

H₀: ? ≤ 50

H_a: ? > 50

A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use

? = 0.05.

(Round your answers to two decimal places.)

(a)

x = 52.3

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that ? > 50.Reject H₀. There is sufficient evidence to conclude that ? > 50. Do not reject H₀. There is insufficient evidence to conclude that ? > 50.Do not reject H₀. There is sufficient evidence to conclude that ? > 50.

(b)

x = 51

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

(c)

x = 51.9

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

Expert Solution

Step 1

The given hypotheses are as follows:

H₀: µ ≤ 50.

H_a: µ > 50.

The sample size is 60 and the population standard deviation is 8. The level of significance is 0.05.

Given that, the sample mean is 52.3.

Obtain the test statistic.

$\begin{array}{rcl} z & = & \frac{x - μ_{0}}{\frac{σ}{\sqrt{n}}} \\ = & \frac{52.3 - 50}{\frac{8}{\sqrt{60}}} \\ = & 2.22696 \\ \approx & 2.2 \end{array}$