### Comparison of Customer Purchases from Old and New Website#### Objective:To compare the proportion of customers who made a purchase from the old website versus the proportion of those who made a purchase from the new website. A simple random sample of customers visiting the old and new websites was taken. The results are shown below:#### Data Summary:| | Old Site | New Site ||----------------|----------------|----------------|| **Successes** | 158 | 57 || **Observations** | 350 | 159 || **p-hat (Sample Proportion)** | 0.451 | 0.358 |#### Statistical Analysis:- **Confidence Level**: 99%- **z-score**: 1.47- **p-value**: 0.142#### Additional Information for Sample Calculation:- Old site samples, \( n_1 \) \( = \)- New site samples, \( n_2 \) \( = \)- Sample proportion for old site samples, \( \hat{p}_1 = \)- Sample proportion for new site samples, \( \hat{p}_2 = \)#### Graphical Representation:The diagram included in the image is a bell curve (normal distribution curve) with marked regions indicating confidence intervals corresponding to the z-scores and p-values mentioned above.##### Key Points:1. The bell curve graph demonstrates the distribution of sample proportions.2. The shaded blue regions represent the rejection regions for extreme values at a 99% confidence level.3. The z-score line indicates at 1.47, and the p-value of 0.142 is marked, showing the likelihood that any observed difference is due to sampling variability.### Interpretation:With a z-score of 1.47 and a p-value of 0.142, this indicates that there is no statistically significant difference between the proportions of customers who made a purchase from the old website compared to the new website, at the 99% confidence level. In other words, the variations observed could be due to random chance rather than a true difference in user behavior between the two sites. For practical purposes, businesses might choose to further investigate other metrics or run additional tests to make more informed decisions regarding site performance.

Answered: Image /qna-images/answer/796a69bb-d123-42ff-9276-36fdb9258771.jpg

n online retailer has a new website and would like to compare the proportion of customers who made a purchase rom the old website versus the proportion who made a purchase from the new website to see if the two proportions are different. A simple random sample of customers visiting the old and new websites is taken. The esults are shown below. Old site New site Successes 158 Successes 57 350 Observations 159 Observations p-hat_1 0.451 p-hat_2 0.358 p= Ex: 1.234 Confidence Level 99% z-score 1.47 p-value 0.142 -3 -2 -1 3 2= Ex: 1.234 Old site samples: n₁ = Ex: 9 New site samples: n₂ = Sample proportion for old site samples: p1 = Ex: 1.234 Sample proportion for new site samples: p2 = 0 1 Z= 2

n online retailer has a new website and would like to compare the proportion of customers who made a purchase rom the old website versus the proportion who made a purchase from the new website to see if the two proportions are different. A simple random sample of customers visiting the old and new websites is taken. The esults are shown below. Old site New site Successes 158 Successes 57 350 Observations 159 Observations p-hat_1 0.451 p-hat_2 0.358 p= Ex: 1.234 Confidence Level 99% z-score 1.47 p-value 0.142 -3 -2 -1 3 2= Ex: 1.234 Old site samples: n₁ = Ex: 9 New site samples: n₂ = Sample proportion for old site samples: p1 = Ex: 1.234 Sample proportion for new site samples: p2 = 0 1 Z= 2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 7PPS

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