Explain the meaning of each term. a. null hypothesis b. alternative hypothesis c. test statistic d. significance level

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Answer 1

Textbook Question

Chapter 9, Problem 1RP

Explain the meaning of each term.

a. null hypothesis
b. alternative hypothesis
c. test statistic
d. significance level

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 + ...

(a)

Expert Solution

To determine

Explain the meaning of null hypothesis.

Explanation of Solution

Null hypothesis:

Null hypothesis is a statement about population parameter, its value is equal to the claim value, which is denoted by H0. The population parameter can be mean, standard deviation, proportion, variance, and so on. The possible symbols used in the null hypothesis would be ≤,≥ or =.

(b)

Expert Solution

To determine

Explain the meaning of alternative hypothesis.

Explanation of Solution

Alternative hypothesis:

It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by Ha.

1. If the sign is < or > then the test is called as one-tailed test.
2. If the sign is ≠. Then the test is called as two-tailed test.

(c)

Expert Solution

To determine

Explain the meaning of test statistic.

Explanation of Solution

Test statistic:

This is a numerical value calculated from sample data by which it can be concluded whether the null hypothesis would be rejected or accepted in a hypothesis testing.

(d)

Expert Solution

To determine

Explain the meaning of level of significance.

Explanation of Solution

Significance level:

The probability of rejecting a true null hypothesis is called as a level of significance.

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Answer 2

Textbook Question

Chapter 9, Problem 1RP

Explain the meaning of each term.

a. null hypothesis
b. alternative hypothesis
c. test statistic
d. significance level

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 + ...

(a)

Expert Solution

To determine

Explain the meaning of null hypothesis.

Explanation of Solution

Null hypothesis:

Null hypothesis is a statement about population parameter, its value is equal to the claim value, which is denoted by H0. The population parameter can be mean, standard deviation, proportion, variance, and so on. The possible symbols used in the null hypothesis would be ≤,≥ or =.

(b)

Expert Solution

To determine

Explain the meaning of alternative hypothesis.

Explanation of Solution

Alternative hypothesis:

It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by Ha.

1. If the sign is < or > then the test is called as one-tailed test.
2. If the sign is ≠. Then the test is called as two-tailed test.

(c)

Expert Solution

To determine

Explain the meaning of test statistic.

Explanation of Solution

Test statistic:

This is a numerical value calculated from sample data by which it can be concluded whether the null hypothesis would be rejected or accepted in a hypothesis testing.

(d)

Expert Solution

To determine

Explain the meaning of level of significance.

Explanation of Solution

Significance level:

The probability of rejecting a true null hypothesis is called as a level of significance.

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Answer 3

Textbook Question

Chapter 9, Problem 1RP

Explain the meaning of each term.

a. null hypothesis
b. alternative hypothesis
c. test statistic
d. significance level

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 + ...

(a)

Expert Solution

To determine

Explain the meaning of null hypothesis.

Explanation of Solution

Null hypothesis:

Null hypothesis is a statement about population parameter, its value is equal to the claim value, which is denoted by H0. The population parameter can be mean, standard deviation, proportion, variance, and so on. The possible symbols used in the null hypothesis would be ≤,≥ or =.

(b)

Expert Solution

To determine

Explain the meaning of alternative hypothesis.

Explanation of Solution

Alternative hypothesis:

It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by Ha.

1. If the sign is < or > then the test is called as one-tailed test.
2. If the sign is ≠. Then the test is called as two-tailed test.

(c)

Expert Solution

To determine

Explain the meaning of test statistic.

Explanation of Solution

Test statistic:

This is a numerical value calculated from sample data by which it can be concluded whether the null hypothesis would be rejected or accepted in a hypothesis testing.

(d)

Expert Solution

To determine

Explain the meaning of level of significance.

Explanation of Solution

Significance level:

The probability of rejecting a true null hypothesis is called as a level of significance.

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Answer 4

Textbook Question

Chapter 9, Problem 1RP

Explain the meaning of each term.

a. null hypothesis
b. alternative hypothesis
c. test statistic
d. significance level

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 + ...

(a)

Expert Solution

To determine

Explain the meaning of null hypothesis.

Explanation of Solution

Null hypothesis:

Null hypothesis is a statement about population parameter, its value is equal to the claim value, which is denoted by H0. The population parameter can be mean, standard deviation, proportion, variance, and so on. The possible symbols used in the null hypothesis would be ≤,≥ or =.

(b)

Expert Solution

To determine

Explain the meaning of alternative hypothesis.

Explanation of Solution

Alternative hypothesis:

It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by Ha.

1. If the sign is < or > then the test is called as one-tailed test.
2. If the sign is ≠. Then the test is called as two-tailed test.

(c)

Expert Solution

To determine

Explain the meaning of test statistic.

Explanation of Solution

Test statistic:

This is a numerical value calculated from sample data by which it can be concluded whether the null hypothesis would be rejected or accepted in a hypothesis testing.

(d)

Expert Solution

To determine

Explain the meaning of level of significance.

Explanation of Solution

Significance level:

The probability of rejecting a true null hypothesis is called as a level of significance.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

Explain the meaning of null hypothesis.

Explanation of Solution

Null hypothesis:

Null hypothesis is a statement about population parameter, its value is equal to the claim value, which is denoted by H0. The population parameter can be mean, standard deviation, proportion, variance, and so on. The possible symbols used in the null hypothesis would be ≤,≥ or =.

(b)

Expert Solution

To determine

Explain the meaning of alternative hypothesis.

Explanation of Solution

Alternative hypothesis:

It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by Ha.

1. If the sign is < or > then the test is called as one-tailed test.
2. If the sign is ≠. Then the test is called as two-tailed test.

(c)

Expert Solution

To determine

Explain the meaning of test statistic.

Explanation of Solution

Test statistic:

This is a numerical value calculated from sample data by which it can be concluded whether the null hypothesis would be rejected or accepted in a hypothesis testing.

(d)

Expert Solution

To determine

Explain the meaning of level of significance.

Explanation of Solution

Significance level:

The probability of rejecting a true null hypothesis is called as a level of significance.

Answer 8

(a)

Expert Solution

To determine

Explain the meaning of null hypothesis.

Explanation of Solution

Null hypothesis:

Null hypothesis is a statement about population parameter, its value is equal to the claim value, which is denoted by H0. The population parameter can be mean, standard deviation, proportion, variance, and so on. The possible symbols used in the null hypothesis would be ≤,≥ or =.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Explain the meaning of null hypothesis.

Answer 13

Explanation of Solution

Null hypothesis:

Null hypothesis is a statement about population parameter, its value is equal to the claim value, which is denoted by H0. The population parameter can be mean, standard deviation, proportion, variance, and so on. The possible symbols used in the null hypothesis would be ≤,≥ or =.

Answer 14

(b)

Expert Solution

To determine

Explain the meaning of alternative hypothesis.

Explanation of Solution

Alternative hypothesis:

It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by Ha.

1. If the sign is < or > then the test is called as one-tailed test.
2. If the sign is ≠. Then the test is called as two-tailed test.

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

To determine

Explain the meaning of alternative hypothesis.

Answer 19

Explanation of Solution

Alternative hypothesis:

It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by Ha.

1. If the sign is < or > then the test is called as one-tailed test.
2. If the sign is ≠. Then the test is called as two-tailed test.

Answer 20

(c)

Expert Solution

To determine

Explain the meaning of test statistic.

Explanation of Solution

Test statistic:

This is a numerical value calculated from sample data by which it can be concluded whether the null hypothesis would be rejected or accepted in a hypothesis testing.

Answer 21

(c)

Expert Solution

Answer 22

(c)

Expert Solution

Answer 23

Expert Solution

Answer 24

To determine

Explain the meaning of test statistic.

Answer 25

Explanation of Solution

Test statistic:

This is a numerical value calculated from sample data by which it can be concluded whether the null hypothesis would be rejected or accepted in a hypothesis testing.