A retailer wants to see if a red "Sale" sign brings in less revenue than the same "Sale" sign in blue. The data below shows the revenue in thousands of dollars that was achieved for various days when the retailer decided to put the red "Sale" sign up and days when the retailer decided to put the blue "Sale" sign up. Red: 2.6, 3.2, 3.4, 1, 2.6, 4.6, 2.7, 3.3, 3.2, 2.4 Blue: 3.7, 4.6, 4.2, 4.1, 3.6, 2.1, 4.7, 3.6 Assume that both populations follow a normal distribution. What can be concluded at the α = 0.05 level of significance level of significance? For this study, we should use?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
A retailer wants to see if a red "Sale" sign brings in less revenue than the same "Sale" sign in blue. The data below shows the revenue in thousands of dollars that was achieved for various days when the retailer decided to put the red "Sale" sign up and days when the retailer decided to put the blue "Sale" sign up.
Red: 2.6, 3.2, 3.4, 1, 2.6, 4.6, 2.7, 3.3, 3.2, 2.4
Blue: 3.7, 4.6, 4.2, 4.1, 3.6, 2.1, 4.7, 3.6
Assume that both populations follow a
For this study, we should use?
- The null and alternative hypotheses would be:
H0: (please enter a decimal)
H1: (Please enter a decimal)
- The test statistic = (please show your answer to 3 decimal places.)
- The p-value = (Please show your answer to 4 decimal places.)
- The p-value is ? α
- Based on this, we should ? the null hypothesis.
- Thus, the final conclusion is that ...
- The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population
mean revenue on days with a red "Sale" sign is less than the population mean revenue on days with a blue "Sale" sign. - The results are statistically insignificant at α = 0.05, so there is statistically significant evidence to conclude that the population mean revenue on days with a red "Sale" sign is equal to the population mean revenue on days with a blue "Sale" sign.
- The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the population mean revenue on days with a red "Sale" sign is less than the population mean revenue on days with a blue "Sale" sign.
- The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the mean revenue for the ten days with a red "Sale" sign is less than the mean revenue for the eight days with a blue "Sale" sign.
- The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population
- Interpret the p-value in the context of the study.
- If the sample mean revenue for the 10 days with a red "Sale" sign is the same as the sample mean revenue for the 8 days with a blue "Sale" sign and if another 10 days with a red "Sale" sign and 8 days with a blue "Sale" sign are observed then there would be a 1.92% chance of concluding that the mean revenue for the 10 days with a red "Sale" sign is at least 0.9 thousand dollars less than the mean revenue for the 8 days with a blue "Sale" sign
- If the population mean revenue on days with a red "Sale" sign is the same as the population mean revenue on days with a blue "Sale" sign and if another 10 days with a red "Sale" sign and 8 days with a blue "Sale" sign are observed then there would be a 1.92% chance that the mean revenue for the 10 days with a red "Sale" sign would be at least 0.9 thousand dollars less than the mean revenue for the 8 days with a blue "Sale" sign.
- There is a 1.92% chance of a Type I error.
- There is a 1.92% chance that the mean revenue for the 10 days with a red "Sale" sign is at least 0.9 thousand dollars less than the mean revenue for the 8 days with a blue "Sale" sign.
- Interpret the level of significance in the context of the study.
- There is a 5% chance that green is your favorite color, so why woud you even consider red or blue?
- There is a 5% chance that there is a difference in the population mean revenue on days with a red "Sale" sign and on days with a blue "Sale" sign.
- If the population mean revenue on days with a red "Sale" sign is the same as the population mean revenue on days with a blue "Sale" sign and if another 10 days with a red "Sale" sign and 8 days with a blue "Sale" sign are observed, then there would be a 5% chance that we would end up falsely concluding that the sample mean revenue for these 10 days with a red "Sale" sign and 8 days with a blue "Sale" sign differ from each other.
- If the population mean revenue on days with a red "Sale" sign is the same as the population mean revenue on days with a blue "Sale" sign and if another 10 days with a red "Sale" sign and 8 days with a blue "Sale" sign are observed then there would be a 5% chance that we would end up falsely concluding that the population mean revenue for the days with a red "Sale" sign is less than the population mean revenue on days with a blue "Sale" sign
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