Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table) H0: μ1 − μ2 ≥ 0 HA: μ1 − μ2 < 0 x−1x−1 = 255 x−2x−2 = 264 s1 = 33 s2 = 15 n1 = 9 n2 = 9 a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) a-2. Find the p-value. multiple choice 1 p-value < 0.01 0.01 %media:le.png% p-value < 0.025 0.025 %media:le.png% p-value < 0.05 0.05 %media:le.png% p-value < 0.10 p-value 0.10 a-3. Do you reject the null hypothesis at the 10% level? multiple choice 2 Yes, since the value of the p-value is less than the significance level. No, since the value of the p-value is less than the significance level. No, since the value of the p-value is greater than the significance level. Yes, since the value of the p-value is greater than the significance level. a-4. Interpret the results at αα = 0.10. multiple choice 3 We conclude that the population means differ. We cannot conclude that the population means differ. We conclude that population mean 1 is less than population mean 2. We cannot conclude that population mean 1 is less than population mean 2. b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) b-2. Find the p-value. multiple choice 4 p-value < 0.01 0.01 %media:le.png% p-value < 0.025 0.025 %media:le.png% p-value < 0.05 0.05 %media:le.png% p-value < 0.10 p-value 0.10 b-3. Do you reject the null hypothesis at the 10% level? multiple choice 5 Yes, since the value of the p-value is less than the significance level. No, since the value of the p-value is greater than the significance level. Yes, since the value of the p-value is greater than the significance level. No, since the value of the p-value is less than the significance level. b-4. Interpret the results at αα = 0.10. multiple choice 6 We conclude that the population means differ. We cannot conclude that the population means differ. We conclude that population mean 1 is less than population mean 2. We cannot conclude that population mean 1 is less than population mean 2.

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table) H0: μ1 − μ2 ≥ 0 HA: μ1 − μ2 < 0 x−1x−1 = 255 x−2x−2 = 264 s1 = 33 s2 = 15 n1 = 9 n2 = 9 a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) a-2. Find the p-value. multiple choice 1 p-value < 0.01 0.01 %media:le.png% p-value < 0.025 0.025 %media:le.png% p-value < 0.05 0.05 %media:le.png% p-value < 0.10 p-value 0.10 a-3. Do you reject the null hypothesis at the 10% level? multiple choice 2 Yes, since the value of the p-value is less than the significance level. No, since the value of the p-value is less than the significance level. No, since the value of the p-value is greater than the significance level. Yes, since the value of the p-value is greater than the significance level. a-4. Interpret the results at αα = 0.10. multiple choice 3 We conclude that the population means differ. We cannot conclude that the population means differ. We conclude that population mean 1 is less than population mean 2. We cannot conclude that population mean 1 is less than population mean 2. b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) b-2. Find the p-value. multiple choice 4 p-value < 0.01 0.01 %media:le.png% p-value < 0.025 0.025 %media:le.png% p-value < 0.05 0.05 %media:le.png% p-value < 0.10 p-value 0.10 b-3. Do you reject the null hypothesis at the 10% level? multiple choice 5 Yes, since the value of the p-value is less than the significance level. No, since the value of the p-value is greater than the significance level. Yes, since the value of the p-value is greater than the significance level. No, since the value of the p-value is less than the significance level. b-4. Interpret the results at αα = 0.10. multiple choice 6 We conclude that the population means differ. We cannot conclude that the population means differ. We conclude that population mean 1 is less than population mean 2. We cannot conclude that population mean 1 is less than population mean 2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table)

H₀: μ₁ − μ₂ ≥ 0
H_A: μ₁ − μ₂ < 0

x−1x−1 = 255	x−2x−2 = 264
s₁ = 33	s₂ = 15
n₁ = 9	n₂ = 9

a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

a-2. Find the p-value.

multiple choice 1

p-value < 0.01
0.01 %media:le.png% p-value < 0.025
0.025 %media:le.png% p-value < 0.05
0.05 %media:le.png% p-value < 0.10
p-value

0.10

a-3. Do you reject the null hypothesis at the 10% level?

multiple choice 2

Yes, since the value of the p-value is less than the significance level.
No, since the value of the p-value is less than the significance level.
No, since the value of the p-value is greater than the significance level.
Yes, since the value of the p-value is greater than the significance level.

a-4. Interpret the results at

αα

= 0.10.

multiple choice 3

We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
We cannot conclude that population mean 1 is less than population mean 2.

b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

multiple choice 4

p-value < 0.01
0.01 %media:le.png% p-value < 0.025
0.025 %media:le.png% p-value < 0.05
0.05 %media:le.png% p-value < 0.10
p-value

0.10

b-3. Do you reject the null hypothesis at the 10% level?

multiple choice 5

Yes, since the value of the p-value is less than the significance level.
No, since the value of the p-value is greater than the significance level.
Yes, since the value of the p-value is greater than the significance level.
No, since the value of the p-value is less than the significance level.

b-4. Interpret the results at

αα

= 0.10.

multiple choice 6

We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
We cannot conclude that population mean 1 is less than population mean 2.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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