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A restaurant manager is concerned about customer complaints regarding the taste of a popular dish, Chicken Alfredo. To address this issue, the chef has been experimenting with two different recipes. Recipe 1 is the traditional and well-established method, while Recipe 2 is a new, cost-effective approach. The restaurant has conducted taste tests with two separate random samples of customers who tried only one each of the recipes. For Recipe 1, the average rating on a scale of 1 to 10 was 7.6, with a standard deviation of 1.1. For Recipe 2, the average rating was 6.7, with a standard deviation of 2.5. Recipe 1 Recipe 2

A restaurant manager is concerned about customer complaints regarding the taste of a popular dish, Chicken Alfredo. To address this issue, the chef has been experimenting with two different recipes. Recipe 1 is the traditional and well-established method, while Recipe 2 is a new, cost-effective approach. The restaurant has conducted taste tests with two separate random samples of customers who tried only one each of the recipes. For Recipe 1, the average rating on a scale of 1 to 10 was 7.6, with a standard deviation of 1.1. For Recipe 2, the average rating was 6.7, with a standard deviation of 2.5. Recipe 1 Recipe 2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
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A restaurant manager is concerned about customer complaints regarding the taste of a popular dish, Chicken Alfredo. To address this issue, the chef has been experimenting with two different recipes. Recipe 1 is the traditional and well-established method, while Recipe 2 is a new, cost-effective approach. The restaurant has conducted taste tests with two separate random samples of customers who tried only one each of the recipes. For Recipe 1, the average rating on a scale of 1 to 10 was 7.6, with a standard deviation of 1.1. For Recipe 2, the average rating was 6.7, with a standard deviation of 2.5. Recipe 1 81780 000 ∞ ∞ O 6 8 8 8 10 7 9 S785∞∞ONONN 9 10 6 6 Recipe 2 10 C 700 OSO OO4 6 2 5 9 8 8 7 5 4 10 5 10 4 6 8 9 3 5 10 10
Transcribed Image Text:A restaurant manager is concerned about customer complaints regarding the taste of a popular dish, Chicken Alfredo. To address this issue, the chef has been experimenting with two different recipes. Recipe 1 is the traditional and well-established method, while Recipe 2 is a new, cost-effective approach. The restaurant has conducted taste tests with two separate random samples of customers who tried only one each of the recipes. For Recipe 1, the average rating on a scale of 1 to 10 was 7.6, with a standard deviation of 1.1. For Recipe 2, the average rating was 6.7, with a standard deviation of 2.5. Recipe 1 81780 000 ∞ ∞ O 6 8 8 8 10 7 9 S785∞∞ONONN 9 10 6 6 Recipe 2 10 C 700 OSO OO4 6 2 5 9 8 8 7 5 4 10 5 10 4 6 8 9 3 5 10 10
The manager is concerned that Recipe 2 may not be as well-received as Recipe 1, and they want to determine if there is a statistically significant difference in customer satisfaction between the two recipes. They need to make an informed decision about whether to continue offering Recipe 2 or stick with the traditional Recipe 1 Using this data set perform the following tasks. Do all calculations 'manually' (i.e., with a hand calculator without using R, Excel, or any other software), showing the relevant formulas and the major steps. Use the sample means and standard deviations provided. (a) Is there statistical evidence that the population variances for both samples are the same? What parametric test can you use to answer this question? Answer using the six steps of hypothesis testing; including by stating the null and alternative hypotheses; providing an appropriate test statistic and its distribution and describing an appropriate decision rule. Implement this test using a 5% significance level. (b) (c) Test if the population mean 'time to failure' of Method 2 is quicker (less) than that of Method 1. Answer using the six steps of hypothesis testing; including by stating the null and alternative hypotheses; providing an appropriate test statistic and its distribution and describing an appropriate decision rule. Implement this test using a 5% significance level. What are the requirements of the hypothesis tests you performed in parts (a) and (b)? Are the requirements about the experimental design, the variable of interest and the measurement scale met? Explain your answers.
Transcribed Image Text:The manager is concerned that Recipe 2 may not be as well-received as Recipe 1, and they want to determine if there is a statistically significant difference in customer satisfaction between the two recipes. They need to make an informed decision about whether to continue offering Recipe 2 or stick with the traditional Recipe 1 Using this data set perform the following tasks. Do all calculations 'manually' (i.e., with a hand calculator without using R, Excel, or any other software), showing the relevant formulas and the major steps. Use the sample means and standard deviations provided. (a) Is there statistical evidence that the population variances for both samples are the same? What parametric test can you use to answer this question? Answer using the six steps of hypothesis testing; including by stating the null and alternative hypotheses; providing an appropriate test statistic and its distribution and describing an appropriate decision rule. Implement this test using a 5% significance level. (b) (c) Test if the population mean 'time to failure' of Method 2 is quicker (less) than that of Method 1. Answer using the six steps of hypothesis testing; including by stating the null and alternative hypotheses; providing an appropriate test statistic and its distribution and describing an appropriate decision rule. Implement this test using a 5% significance level. What are the requirements of the hypothesis tests you performed in parts (a) and (b)? Are the requirements about the experimental design, the variable of interest and the measurement scale met? Explain your answers.
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