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Consumer Reports uses a 100-point customer satisfaction score to rate the nation's major chain stores. Assume that from past experience with the satisfaction rating score, a population standard deviation of 12 is expected. Costco with its 432 warehouses in 40 states was the only chain store to earn an outstanding rating for overall quality. A sample of 15 Costco customer satisfaction scores is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions. Open spreadsheet a. What is the sample mean customer satisfaction score for Costco (to 2 decimals)? b. What is the sample variance (to 2 decimals)? c. What is the sample standard deviation (to 2 decimals)? d. Construct a hypothesis test to determine whether the population standard deviation of 12 should be rejected for Costco. State the null and alternative hypotheses. H₂=144 H₁: 144 Calculate the value of the test statistic (to 2 decimals). p-value is With a .05 level of significance, what is your conclusion? The hypothesis that the population standard deviation is 12 [cannot be rejected

Consumer Reports uses a 100-point customer satisfaction score to rate the nation's major chain stores. Assume that from past experience with the satisfaction rating score, a population standard deviation of 12 is expected. Costco with its 432 warehouses in 40 states was the only chain store to earn an outstanding rating for overall quality. A sample of 15 Costco customer satisfaction scores is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions. Open spreadsheet a. What is the sample mean customer satisfaction score for Costco (to 2 decimals)? b. What is the sample variance (to 2 decimals)? c. What is the sample standard deviation (to 2 decimals)? d. Construct a hypothesis test to determine whether the population standard deviation of 12 should be rejected for Costco. State the null and alternative hypotheses. H₂=144 H₁: 144 Calculate the value of the test statistic (to 2 decimals). p-value is With a .05 level of significance, what is your conclusion? The hypothesis that the population standard deviation is 12 [cannot be rejected

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Consumer Reports** uses a 100-point customer satisfaction score to rate the nation's major chain stores. Assume that from past experience with the satisfaction rating score, a population standard deviation of σ = 12 is expected. Costco, with its 432 warehouses in 40 states, was the only chain store to earn an outstanding rating for overall quality. A sample of 15 Costco customer satisfaction scores is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions. **a.** What is the sample mean customer satisfaction score for Costco (to 2 decimals)? \[ \_\_\_\_\_ \] **b.** What is the sample variance (to 2 decimals)? \[ \_\_\_\_\_ \] **c.** What is the sample standard deviation (to 2 decimals)? \[ \_\_\_\_\_ \] **d.** Construct a hypothesis test to determine whether the population standard deviation of σ = 12 should be rejected for Costco. **State the null and alternative hypotheses.** \[ H_0 : \sigma^2 = 144 \] \[ H_1 : \sigma^2 \neq 144 \] Calculate the value of the test statistic (to 2 decimals). \[ \text{Test Statistic} = \_\_\_\_\_ \] \[ \text{p-value} = \_\_\_\_\_ \] With a .05 level of significance, what is your conclusion? The hypothesis that the population standard deviation is 12 \[ \text{cannot be rejected} \] ✅.
Transcribed Image Text:**Consumer Reports** uses a 100-point customer satisfaction score to rate the nation's major chain stores. Assume that from past experience with the satisfaction rating score, a population standard deviation of σ = 12 is expected. Costco, with its 432 warehouses in 40 states, was the only chain store to earn an outstanding rating for overall quality. A sample of 15 Costco customer satisfaction scores is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions. **a.** What is the sample mean customer satisfaction score for Costco (to 2 decimals)? \[ \_\_\_\_\_ \] **b.** What is the sample variance (to 2 decimals)? \[ \_\_\_\_\_ \] **c.** What is the sample standard deviation (to 2 decimals)? \[ \_\_\_\_\_ \] **d.** Construct a hypothesis test to determine whether the population standard deviation of σ = 12 should be rejected for Costco. **State the null and alternative hypotheses.** \[ H_0 : \sigma^2 = 144 \] \[ H_1 : \sigma^2 \neq 144 \] Calculate the value of the test statistic (to 2 decimals). \[ \text{Test Statistic} = \_\_\_\_\_ \] \[ \text{p-value} = \_\_\_\_\_ \] With a .05 level of significance, what is your conclusion? The hypothesis that the population standard deviation is 12 \[ \text{cannot be rejected} \] ✅.
**Satisfaction Score Analysis** This spreadsheet provides a framework for analyzing satisfaction scores using statistical methods. Below is an explanation of each section and the required calculations: ### Data - **Satisfaction Scores**: - 93, 90, 85, 77, 95, 98, 80, 83, 93, 89, 80, 97, 67, 66 ### Statistical Analysis #### Part a: Mean - **Mean**: Calculate the average of the satisfaction scores. #### Part b: Variance - **Variance**: Measure the degree of variation in the scores. #### Part c: Standard Deviation - **Standard Deviation**: Calculate the dispersion of the dataset relative to the mean. #### Part d: Degrees of Freedom - **Degrees of Freedom**: Number of values in the final calculation of a statistic that are free to vary. ### Hypothesis Testing - **Hypothesized Standard Deviation**: 12 - **Chi Square Test Statistics**: Calculate based on hypothesized standard deviation. ### P-values - **Lower-Tail p-value**: Probability of the statistic falling below a certain value. - **Upper-Tail p-value**: Probability of the statistic being above a certain value. - **Two-Tail p-value**: Probability of the statistic being in either tail. - **Significance Level (alpha)**: 0.05 ### Hypothesis Decision - **Question**: Can the hypothesis that the population standard deviation is 12 be rejected? - **Output**: Enter "Can be rejected" or "Cannot be rejected" based on the analysis. ### Graphs and Diagrams There are no graphs or diagrams included in this spreadsheet. This structured approach helps in assessing whether the population standard deviation deviates significantly from the hypothesized value of 12, using statistical tests like Chi-Square.
Transcribed Image Text:**Satisfaction Score Analysis** This spreadsheet provides a framework for analyzing satisfaction scores using statistical methods. Below is an explanation of each section and the required calculations: ### Data - **Satisfaction Scores**: - 93, 90, 85, 77, 95, 98, 80, 83, 93, 89, 80, 97, 67, 66 ### Statistical Analysis #### Part a: Mean - **Mean**: Calculate the average of the satisfaction scores. #### Part b: Variance - **Variance**: Measure the degree of variation in the scores. #### Part c: Standard Deviation - **Standard Deviation**: Calculate the dispersion of the dataset relative to the mean. #### Part d: Degrees of Freedom - **Degrees of Freedom**: Number of values in the final calculation of a statistic that are free to vary. ### Hypothesis Testing - **Hypothesized Standard Deviation**: 12 - **Chi Square Test Statistics**: Calculate based on hypothesized standard deviation. ### P-values - **Lower-Tail p-value**: Probability of the statistic falling below a certain value. - **Upper-Tail p-value**: Probability of the statistic being above a certain value. - **Two-Tail p-value**: Probability of the statistic being in either tail. - **Significance Level (alpha)**: 0.05 ### Hypothesis Decision - **Question**: Can the hypothesis that the population standard deviation is 12 be rejected? - **Output**: Enter "Can be rejected" or "Cannot be rejected" based on the analysis. ### Graphs and Diagrams There are no graphs or diagrams included in this spreadsheet. This structured approach helps in assessing whether the population standard deviation deviates significantly from the hypothesized value of 12, using statistical tests like Chi-Square.
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