SOLUTION: Question 3 (20 marks) 3(a)The Sales manager at Hybrid Industries a high-tech farming agency claims that there has been a drop in the sales from the target of $2800/- per week. D

Question 1179172: Question 3 (20 marks)
3(a)The Sales manager at Hybrid Industries a high-tech farming agency
claims that there has been a drop in the sales from the target of $2800/- per
week. Data was collected for the last 48 weeks and the sample mean was
computed as $ 2435/- with a SD $ 351. Verify at 5% los if the manager’s
claim can be accepted based on the sample observations.

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to conduct a hypothesis test to verify the sales manager's claim:
**1. State the Hypotheses:**
* **Null Hypothesis (H0):** The population mean sales are equal to or greater than $2800 (μ ≥ 2800).
* **Alternative Hypothesis (H1):** The population mean sales are less than $2800 (μ < 2800).
This is a left-tailed test.
**2. Set the Significance Level:**
* α = 0.05 (5%)
**3. Choose the Test Statistic:**
* Since the population standard deviation is unknown and the sample size is large (n = 48 > 30), we will use a z-test.
**4. Calculate the Test Statistic (z-score):**
* Sample mean (x̄): $2435
* Population mean (μ): $2800
* Sample standard deviation (s): $351
* Sample size (n): 48
z = (x̄ - μ) / (s / √n)
z = (2435 - 2800) / (351 / √48)
z = -365 / (351 / 6.928)
z = -365 / 50.66
z ≈ -7.20
**5. Find the Critical Value:**
* For a left-tailed test with α = 0.05, the critical z-value is -1.645. (You can find this using a z-table or calculator).
**6. Make a Decision:**
* Compare the calculated z-score (-7.20) to the critical z-value (-1.645).
* Since -7.20 < -1.645, the calculated z-score falls in the rejection region.
* Therefore, we reject the null hypothesis.
**7. Draw a Conclusion:**
* There is sufficient evidence at the 5% significance level to support the sales manager's claim that there has been a drop in sales from the target of $2800 per week.
**In summary:**
The calculated z-score of -7.20 is far into the rejection region of the left tailed test. Therefore we can confidently reject the null hypothesis and accept the sales managers claim.

RELATED QUESTIONS
The Sales manager at Hybrid Industries a high tech farming agency claims that there has... (answered by Boreal)

Question 1 The Sales manager at Hybrid Industries a high tech farming agency claims that... (answered by Boreal)

Nicole has been offered a sales job at High Tech and a sales job at Best Computers. Which (answered by ReadingBoosters)

A farming cooperative in the KwaMashu buys wheat seeds for its farmer members from seed... (answered by ikleyn)

2.1 What determines use of t-distribution and z-distribution in confidence interval... (answered by ikleyn)

A farming cooperative in the KwaMashu buys wheat seeds for its farmer members from seed... (answered by Boreal,Theo)

Good day. please help me solve this problem. The table below lists the distribution of... (answered by Edwin McCravy,ikleyn)

A salesman paid 12 visits to his area sales manager and noted that he had to wait for... (answered by richwmiller)

A salesman paid 12 visits to his area sales manager and noted that he had to wait for... (answered by ewatrrr)