How is it done please show step by step ## Hypothesis Testing for Mean Daily Sales Difference### Problem StatementBased on the data provided, can the owner conclude, at the 0.01 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding \( \mu_d \) (which is \( \mu \) with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is normally distributed.**Data Provided:**| | Store 1 | Store 2 | Difference (Store 1 - Store 2) ||--------|---------|---------|------------------------------|| Sales | 797 | 733 | 64 || | 553 | 498 | 55 || | 742 | 509 | 233 || | 580 | 741 | -161 || | 632 | 632 | 0 || | 758 | 484 | 274 || | 832 | 758 | 74 |### Steps to Perform Hypothesis Test1. **State the Hypotheses:** - **Null Hypothesis (\( H_0 \))**: There is no difference in the mean daily sales between the two stores. (\( \mu_d = 0 \)) - **Alternative Hypothesis (\( H_1 \))**: There is a difference in the mean daily sales between the two stores. (\( \mu_d \neq 0 \))2. **Determine the Type of Test Statistic:** - The choice of the test statistic depends on the sample size and data distribution. Common options include t-test or z-test.3. **Calculate the Test Statistic:** - Compute the test statistic based on the provided data. This involves calculating the sample mean difference, standard deviation of the differences, and then applying the appropriate formula for the t-test.4. **Find the Critical Values:** - Determine the critical values at the 0.01 level of significance for a two-tailed test.5. **Conclusion:** - Based on the test statistic and critical values, decide whether to reject the null hypothesis.### Form Inputs(a) **State the null hypothesis \( H ### Analyzing Sales Performance of Two Stores: A Hypothesis Test#### Sales Data for AnalysisThe owner of a chain of minimarkets wishes to compare the sales performance of two stores, Store 1 and Store 2. Sales can fluctuate significantly depending on the day of the week and the time of year, so the owner decides to eliminate such effects by recording each store's sales on the same 8 days chosen at random. The table below displays the sales (in dollars) for each store on these 8 days:| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 ||-----|-----|-----|-----|-----|-----|-----|------|------|| Store 1 | 797 | 553 | 719 | 756 | 648 | 751 | 697 | 214 || Store 2 | 733 | 498 | 741 | 737 | 633 | 678 | 558 | 140 || Difference (Store 1 - Store 2) | 64 | 55 | -22 | 19 | 15 | 73 | 139 | 74 |Based on this data, one can perform a hypothesis test to determine if the mean daily sales of the two stores differ at a 0.01 level of significance. Assume that the population of differences between Store 1 and Store 2's sales is normally distributed. Follow the steps below to complete the hypothesis test.#### Steps to Perform Hypothesis Testing1. **State the Hypotheses:** - **Null Hypothesis (H₀):** The mean difference in daily sales between Store 1 and Store 2 (µ₁ - µ₂) is zero. - **Alternative Hypothesis (H₁):** The mean difference in daily sales between Store 1 and Store 2 (µ₁ - µ₂) is not zero.2. **Determine the Type of Test Statistic:** - Choose the appropriate test statistic based on the given data. For this scenario, the t-statistic is typically used for small sample sizes when the population variance is unknown.3. **Find the Value of the Test Statistic:** - Calculate the t-statistic using the sample data. Round the value to three

Given : The mean daily sales and the differences between the two stores is given below: Store 2…

Store 2 733 498 509 741 632 484 758 140 Difference 64 55 (Store 1 - Store 2) 233 38 -76 164 149 74 Send data to calculator ed on these data, can the owner conclude, at the 0.01 level of significance, that the mean daily sales of the two stores differ? Answer this question by forming a hypothesis test regarding Hd (which is u with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume at this population of differences (Store 1 minus Store 2) is normally distributed. form a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as ecified. (If necessary, consult a list of formulas.) a) State the null hypothesis Ho and the alternative hypothesis H₁. μ Р Ho :O H₁ [ (b) Determine the type of test statistic to use. Type of test statistic: (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) decimal places Ix 4 a S X 2 Olo 0=0 OSO 20 >O ☐☐ □<口

Store 2 733 498 509 741 632 484 758 140 Difference 64 55 (Store 1 - Store 2) 233 38 -76 164 149 74 Send data to calculator ed on these data, can the owner conclude, at the 0.01 level of significance, that the mean daily sales of the two stores differ? Answer this question by forming a hypothesis test regarding Hd (which is u with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume at this population of differences (Store 1 minus Store 2) is normally distributed. form a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as ecified. (If necessary, consult a list of formulas.) a) State the null hypothesis Ho and the alternative hypothesis H₁. μ Р Ho :O H₁ [ (b) Determine the type of test statistic to use. Type of test statistic: (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) decimal places Ix 4 a S X 2 Olo 0=0 OSO 20 >O ☐☐ □<口

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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How is it done please show step by step

## Hypothesis Testing for Mean Daily Sales Difference

### Problem Statement

Based on the data provided, can the owner conclude, at the 0.01 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding \( \mu_d \) (which is \( \mu \) with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is normally distributed.

**Data Provided:**

| | Store 1 | Store 2 | Difference (Store 1 - Store 2) |
|--------|---------|---------|------------------------------|
| Sales | 797 | 733 | 64 |
| | 553 | 498 | 55 |
| | 742 | 509 | 233 |
| | 580 | 741 | -161 |
| | 632 | 632 | 0 |
| | 758 | 484 | 274 |
| | 832 | 758 | 74 |

### Steps to Perform Hypothesis Test

1. **State the Hypotheses:**
- **Null Hypothesis (\( H_0 \))**: There is no difference in the mean daily sales between the two stores. (\( \mu_d = 0 \))
- **Alternative Hypothesis (\( H_1 \))**: There is a difference in the mean daily sales between the two stores. (\( \mu_d \neq 0 \))

2. **Determine the Type of Test Statistic:**
- The choice of the test statistic depends on the sample size and data distribution. Common options include t-test or z-test.

3. **Calculate the Test Statistic:**
- Compute the test statistic based on the provided data. This involves calculating the sample mean difference, standard deviation of the differences, and then applying the appropriate formula for the t-test.

4. **Find the Critical Values:**
- Determine the critical values at the 0.01 level of significance for a two-tailed test.

5. **Conclusion:**
- Based on the test statistic and critical values, decide whether to reject the null hypothesis.

### Form Inputs

(a) **State the null hypothesis \( H

### Analyzing Sales Performance of Two Stores: A Hypothesis Test

#### Sales Data for Analysis
The owner of a chain of minimarkets wishes to compare the sales performance of two stores, Store 1 and Store 2. Sales can fluctuate significantly depending on the day of the week and the time of year, so the owner decides to eliminate such effects by recording each store's sales on the same 8 days chosen at random. The table below displays the sales (in dollars) for each store on these 8 days:

| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|-----|-----|-----|-----|-----|-----|-----|------|------|
| Store 1 | 797 | 553 | 719 | 756 | 648 | 751 | 697 | 214 |
| Store 2 | 733 | 498 | 741 | 737 | 633 | 678 | 558 | 140 |
| Difference (Store 1 - Store 2) | 64 | 55 | -22 | 19 | 15 | 73 | 139 | 74 |

Based on this data, one can perform a hypothesis test to determine if the mean daily sales of the two stores differ at a 0.01 level of significance. Assume that the population of differences between Store 1 and Store 2's sales is normally distributed. Follow the steps below to complete the hypothesis test.

#### Steps to Perform Hypothesis Testing
1. **State the Hypotheses:**
- **Null Hypothesis (H₀):** The mean difference in daily sales between Store 1 and Store 2 (µ₁ - µ₂) is zero.
- **Alternative Hypothesis (H₁):** The mean difference in daily sales between Store 1 and Store 2 (µ₁ - µ₂) is not zero.

2. **Determine the Type of Test Statistic:**
- Choose the appropriate test statistic based on the given data. For this scenario, the t-statistic is typically used for small sample sizes when the population variance is unknown.

3. **Find the Value of the Test Statistic:**
- Calculate the t-statistic using the sample data. Round the value to three

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