The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same 8 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. Day Store 1 Store 2 Difference (Store 1 - Store 2) Send data to calculator 1 2 467 865 361 3 4 903 102 5 254 704 929 611 671 106 -38 152 93 258 6 418 734 550 - 132 7 737 (a) State the null hypothesis Ho and the alternative hypothesis H₁. H :D -3 8 621 690 - 69 Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding μd (which is u 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. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.) H Y O S Р Â
The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same 8 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. Day Store 1 Store 2 Difference (Store 1 - Store 2) Send data to calculator 1 2 467 865 361 3 4 903 102 5 254 704 929 611 671 106 -38 152 93 258 6 418 734 550 - 132 7 737 (a) State the null hypothesis Ho and the alternative hypothesis H₁. H :D -3 8 621 690 - 69 Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding μd (which is u 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. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.) H Y O S Р Â
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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Transcribed Image Text:The image shows a table and some accompanying text designed for statistical analysis.
**Table Description:**
- **Columns:**
- Day numbers from 1 to 8.
- **Rows:**
- *Store 1 Sales:* 467, 865, 254, 704, 929, 418, 734, 621
- *Store 2 Sales:* 361, 903, 102, 611, 671, 550, 737, 690
- *Difference (Store 1 - Store 2):* 106, -38, 152, 93, 258, -132, -3, -69
The table is used to compare daily sales for two mini-markets over eight random days. The 'Difference' row calculates the difference in sales between Store 1 and Store 2 for each day.
**Text Instructions:**
The task is to determine if the mean daily sales of the two stores differ significantly at a 0.10 level of significance. This involves:
- Conducting a hypothesis test regarding \(\mu_d\), the population mean daily sales difference.
- Assuming the population of differences is normally distributed.
- Performing a two-tailed test.
Additionally, the steps involve:
1. Stating the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\).
2. Using precise computations rounded to three or more decimal places.
The image provides fields for entering hypotheses and includes options for explanations and checking answers.
The educational objective is to understand hypothesis testing, specifically using a paired sample t-test in statistics.
 \( H_0 \) and the [alternative hypothesis](#) \( H_1 \).
- \( H_0 : \) \[ \_\_\_\_\_\_ \]
- \( H_1 : \) \[ \_\_\_\_\_\_ \]
**(b)** Determine the type of [test statistic](#) to use.
- Type of test statistic: \[ \text{Choose one} \]
**(c)** Find the value of the test statistic. (Round to three or more decimal places.)
- \[ \_\_\_\_\_\_ \]
**(d)** Find the two [critical values](#) at the 0.10 level of significance. (Round to three or more decimal places.)
- \[ \_\_\_\_\_\_ \] and \[ \_\_\_\_\_\_ \]
**(e)** At the 0.10 level, can the owner conclude that the mean daily sales of the two stores differ?
- \[ \text{Yes} \; \Box \; \text{No} \; \Box \]
**Buttons for User Interaction:**
- **Explanation**
- **Check**
---
**Side Panel Notes:**
- Symbols include \(\mu, \sigma, \bar{x}, s\).
- Diagrams represent different statistical distributions and tests.
**Legal Notice:** © 2022 McGraw Hill LLC. All Rights Reserved. [Terms of Use](#)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79bed478-1fd0-43ea-baec-0803498e5e8e%2F3659069a-2744-4e3a-b05a-3b2a8349b252%2Fhoni1zo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Transcription for Educational Website:
---
### Hypothesis Testing Exercise
**Instructions**: Fill in the blanks with the appropriate values or selections to complete the hypothesis test for the given problem.
**(a)** State the [null hypothesis](#) \( H_0 \) and the [alternative hypothesis](#) \( H_1 \).
- \( H_0 : \) \[ \_\_\_\_\_\_ \]
- \( H_1 : \) \[ \_\_\_\_\_\_ \]
**(b)** Determine the type of [test statistic](#) to use.
- Type of test statistic: \[ \text{Choose one} \]
**(c)** Find the value of the test statistic. (Round to three or more decimal places.)
- \[ \_\_\_\_\_\_ \]
**(d)** Find the two [critical values](#) at the 0.10 level of significance. (Round to three or more decimal places.)
- \[ \_\_\_\_\_\_ \] and \[ \_\_\_\_\_\_ \]
**(e)** At the 0.10 level, can the owner conclude that the mean daily sales of the two stores differ?
- \[ \text{Yes} \; \Box \; \text{No} \; \Box \]
**Buttons for User Interaction:**
- **Explanation**
- **Check**
---
**Side Panel Notes:**
- Symbols include \(\mu, \sigma, \bar{x}, s\).
- Diagrams represent different statistical distributions and tests.
**Legal Notice:** © 2022 McGraw Hill LLC. All Rights Reserved. [Terms of Use](#)
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