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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Question

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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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