Having some trouble on part D with sample distribution mean and deviation, thank you. ### Analyzing Differences in Annoyances Between Males and Females: A Hypothesis Test on Sample Proportions#### Research Scenario:Researchers aimed to investigate whether there is a difference between males and females in terms of common annoyances, specifically related to people who continuously check their mobile phones during in-person conversations. The data collected were from a random sample where 524 males and 511 females were surveyed. Among the males, 204 responded "Yes," indicating annoyance, while among the females, 215 responded "Yes."#### The Investigation:Does the evidence suggest a higher proportion of females are annoyed by this behavior? The hypothesis testing is conducted in several steps as outlined below:#### (a) Determining Sample Proportions:The sample proportions of annoyed individuals in each group are as follows:- Proportion of annoyed females: \( \hat{p}_1 = 0.4207 \)- Proportion of annoyed males: \( \hat{p}_2 = 0.3893 \)*(Note: These proportions are rounded to four decimal places.)*#### (b) Suitability of Hypothesis Testing Method:To determine if the hypothesis test regarding two independent proportions is applicable, the following criteria must be checked:- **A**: The sample size is less than 5% of the population size for each sample. \( \checked \)- **B**: \( n_1 \hat{p}_1 (1 - \hat{p}_1) \ge 10 \) and \( n_2 \hat{p}_2 (1 - \hat{p}_2) \ge 10 \). \( \checked \)- **C**: The samples are dependent. \( \square \)- **D**: The samples are independent. \( \checked \)- **E**: The data come from a population that is normally distributed. \( \square \)- **F**: The sample size is more than 5% of the population size for each sample. \( \square \)Selected conditions that apply: A, B, and D.#### (c) Null and Alternative Hypotheses:To test the difference in annoyance levels between females and males:- Null Hypothesis (\( H_0 \)): \( p_1 = p_2 \)- Alternative Hypothesis (\( H_1 \)): \( p_1 > p_2 \)Here, \(

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Researchers wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and females, the following question: "Are you annoyed by people who repeatedly check their mobile phones while having an in-person conversation?" Among the 524 males surveyed, 204 responded "Yes"; among the 511 females surveyed, 215 responded "Yes." Does the evidence suggest a higher proportion of females are annoyed by this behavior? Complete parts (a) through (g) below. (a) Determine the sample proportion for each sample. The proportions of the females and males who took the survey who are annoyed by the behavior in question are 0.4207 and 0.3893, respectively. (Round to four decimal places as needed.) (b) Explain why this study can be analyzed using the methods for conducting a hypothesis test regarding two independent proportions. Select all that apply. A. The sample size is less than 5% of the population size for each sample. B. n₁P₁ (1-₁) 210 and n₂P2 (1-P₂) ≥10 C. The samples are dependent. D. The samples are independent. E. The data come from a population that is normally distributed. F. The sample size is more than 5% of the population size for each sample. (c) What are the null and alternative hypotheses? Let p, represent the population proportion females who are annoyed by the behavior in question and p₂ represent the population proportion of males who are annoyed by the behavior in question. Ho: P₁ P₂ H₁: P₁ P₂ (d) Describe the sampling distribution of Pfemale - Pmale-Draw a normal model with the area representing the P-value shaded for this hypothesis test. The sampling distribution is approximately normal with mean and standard deviation. (Type an integer or decimal rounded to four decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Having some trouble on part D with sample distribution mean and deviation, thank you.

### Analyzing Differences in Annoyances Between Males and Females: A Hypothesis Test on Sample Proportions

#### Research Scenario:
Researchers aimed to investigate whether there is a difference between males and females in terms of common annoyances, specifically related to people who continuously check their mobile phones during in-person conversations. The data collected were from a random sample where 524 males and 511 females were surveyed. Among the males, 204 responded "Yes," indicating annoyance, while among the females, 215 responded "Yes."

#### The Investigation:
Does the evidence suggest a higher proportion of females are annoyed by this behavior? The hypothesis testing is conducted in several steps as outlined below:

#### (a) Determining Sample Proportions:
The sample proportions of annoyed individuals in each group are as follows:
- Proportion of annoyed females: \( \hat{p}_1 = 0.4207 \)
- Proportion of annoyed males: \( \hat{p}_2 = 0.3893 \)

*(Note: These proportions are rounded to four decimal places.)*

#### (b) Suitability of Hypothesis Testing Method:
To determine if the hypothesis test regarding two independent proportions is applicable, the following criteria must be checked:
- **A**: The sample size is less than 5% of the population size for each sample. \( \checked \)
- **B**: \( n_1 \hat{p}_1 (1 - \hat{p}_1) \ge 10 \) and \( n_2 \hat{p}_2 (1 - \hat{p}_2) \ge 10 \). \( \checked \)
- **C**: The samples are dependent. \( \square \)
- **D**: The samples are independent. \( \checked \)
- **E**: The data come from a population that is normally distributed. \( \square \)
- **F**: The sample size is more than 5% of the population size for each sample. \( \square \)

Selected conditions that apply: A, B, and D.

#### (c) Null and Alternative Hypotheses:
To test the difference in annoyance levels between females and males:
- Null Hypothesis (\( H_0 \)): \( p_1 = p_2 \)
- Alternative Hypothesis (\( H_1 \)): \( p_1 > p_2 \)

Here, \(

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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