A sales manager for a large department store believes that customer spending per visit with a sale is lower than customer spending without a sale and would like to test that claim. A simple random sample of customer spending is taken from visits without a sale and with a sale. The results are shown below.| | Without sale | With sale ||-------------------|--------------|-----------|| **Mean** | 82.904 | 71.316 || **Variance** | 1984.96 | 1826.41 || **Observations** | 200 | 150 || **Hypothesized Mean Difference** | 0 | || **df** | 328 | || **t Stat** | -2.465 | || **P(T<=t) one-tail** | 0.0071 | || **t Critical one-tail** | -1.65 | || **P(T<=t) two-tail** | 0.0142 | || **t Critical two-tail** | -1.967 | || **Confidence Level** | 99% | |**Graph Explanation:**The graph is a bell-shaped curve illustrating a normal distribution with a blue shaded area on the left tail, indicating the critical region for a one-tailed t-test. The x-axis is labeled from -3 to 3, corresponding to t-scores. The curve is symmetric around zero.**Equations:**- Samples from without sale: $ n_{\text{without}} = $ Ex: 9- Samples from with sale: $ n_{\text{with}} = $ - Point estimate for spending without sale: $ \bar{x}_{\text{without}} = $ Ex: 1.234- Point estimate for spending with sale: $ \bar{x}_{\text{with}} = $ - $ p = $ Ex: 1.234- $ t = $ This analysis aims to determine if there is a statistically significant difference in spending between customers visiting during sales versus those who do not.

Answered: A sales manager for a large department…

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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An online math tutor service would like to claim that the average time spent taking a standardized test after students go through tutoring is less than the average time spent before going through tutoring. A simple random sample of students takes a pre-test, then goes through tutoring and takes a post-test. Results of the sample are shown below. Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Confidence Level Before After 82.333 74.944 110.118 199.820 18 0.727 18 0 17 -3.227 0.002 -1.740 0.005 -2.110 99% What are the population parameters? Pick Is the two-sample hypothesis test a paired t-test or an unpaired t-test? Pick What is the level of significance? Ex: 0.12 What is the null hypothesis? Ho: Mafter Pick Mbefore What is the alternative hypothesis? Ha : Pafter Pick Should Ho be rejected or does Ho fail to be rejected? Pick What conclusion can be drawn from the data? Pick…
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