### Hypothesis Testing for the Difference Between Two Population Means#### ScenarioA company that develops an automated customer service model seeks to determine whether two versions, Version A and Version B, will receive different ratings from customers. Participants in a focus group are exposed to samples from both versions, followed by a survey to rate each version. Below is a summary of the data obtained from the study. The study assumes that ratings from the different surveys generally have the same standard deviation.#### Data Summary| Statistic | Version A | Version B ||---------------------------------|-----------|-----------|| Mean | 33.133 | 28.67 || Observations | 15 | 15 || Pearson Correlation | -0.325 | - || Hypothesized Mean Difference | 0.00 | - || Degrees of Freedom (df) | 14 | - || t Stat | -1.426 | - || P(T≤t) one-tail | 0.088 | - || t Critical one-tail | -1.345 | - || P(T≤t) two-tail | 0.176 | - || t Critical two-tail | -1.761 | - || Confidence Level | 95% | - |#### Explanation of the Data- **Mean**: The average rating for Version A is 33.133 and for Version B is 28.67.- **Observations**: Both versions had 15 participants each.- **Pearson Correlation**: Correlation between the two ratings is -0.325.- **Hypothesized Mean Difference**: Assumed to be 0.00 for testing purposes.- **Degrees of Freedom (df)**: Calculated as 14.- **t Stat**: The computed t-value for the test statistic is -1.426.- **P(T≤t) one-tail**: The p-value for a one-tailed test is 0.088.- **t Critical one-tail**: The critical t-value for a one-tailed test at a 95% confidence level is -1.345.- **P(T≤t) two-tail**: The p-value for a two-tailed test is 0.176.- **t Critical two-tail

The hypothesis test for the difference between two population means is,

A company that develops an automated customer service model is interested in knowing whether two versions, Version A and Version B, will get different ratings from customers. Participants in a focus group are taken through samples from both versions, then take a survey to rate each version. A summary of the data obtained from the study is given below. Assume ratings from the different surveys generally have the same standard deviation. Version A Version B Mean 33.133 28.67 15 15 Observations Pearson Correlation Hypothesized Mean Difference -0.325 0.00 df 14 t Stat -1.426 P(T<=t) one-tail 0.088 P= Ex: 1.234 t Critical one-tail -1.345 P(T<=t) two-tail 0.176 -1.761 t Critical two-tail Confidence Level 95% -3 -2 -1 3 t = Ex: 1.234 n = Ex: 9 Degrees of freedom: df = Point estimate for Version A: 1 = Ex: 1234 Point estimate for Version B: X₂ = 0 1 t=

A company that develops an automated customer service model is interested in knowing whether two versions, Version A and Version B, will get different ratings from customers. Participants in a focus group are taken through samples from both versions, then take a survey to rate each version. A summary of the data obtained from the study is given below. Assume ratings from the different surveys generally have the same standard deviation. Version A Version B Mean 33.133 28.67 15 15 Observations Pearson Correlation Hypothesized Mean Difference -0.325 0.00 df 14 t Stat -1.426 P(T<=t) one-tail 0.088 P= Ex: 1.234 t Critical one-tail -1.345 P(T<=t) two-tail 0.176 -1.761 t Critical two-tail Confidence Level 95% -3 -2 -1 3 t = Ex: 1.234 n = Ex: 9 Degrees of freedom: df = Point estimate for Version A: 1 = Ex: 1234 Point estimate for Version B: X₂ = 0 1 t=

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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