QUESTION 13
An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important
to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 120 clients of an
online stock trading company, the average number of trades per year was 82 with a standard deviation of 16 . If you were to test
the hypothesis that the average number of trades per year is different than the previous year when the average number of trades
was 85 (using the level of significance), what is p-value for this test? (please round your answer to 4 decimal places)

Question

QUESTION 13
An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important
to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 120 clients of an
online stock trading company, the average number of trades per year was 82 with a standard deviation of 16 . If you were to test
the hypothesis that the average number of trades per year is different than the previous year when the average number of trades
was 85 (using the

level of significance), what is p-value for this test? (please round your answer to 4 decimal places)

UpStudy AI · Accepted Answer

To determine the p-value for testing whether the average number of trades per year has changed from the previous year, follow these steps:

### **Given:**
- **Sample size (n):** 120
- **Sample mean ($$\bar{x}$$):** 82
- **Population mean under null hypothesis ($$\mu_0$$):** 85
- **Sample standard deviation (s):** 16
- **Significance level:** 5% (two-tailed test)

### **Steps:**

1. **Formulate Hypotheses:**
   - **Null Hypothesis ($$H_0$$):** $$\mu = 85$$
   - **Alternative Hypothesis ($$H_1$$):** $$\mu \neq 85$$

2. **Calculate the Test Statistic (z):**
   $$
   z = \frac{\bar{x} - \mu_0}{s / \sqrt{n}} = \frac{82 - 85}{16 / \sqrt{120}} = \frac{-3}{1.4606} \approx -2.054
   $$

3. **Determine the p-value:**
   - Since this is a two-tailed test, the p-value is $$2 \times P(Z < -2.054)$$.
   - Using standard normal distribution tables or a calculator:
     $$
     P(Z < -2.054) \approx 0.0200
     $$
   - Therefore, the p-value is:
     $$
     2 \times 0.0200 = 0.0400
     $$

### **Conclusion:**
The p-value for this test is **0.0400**. Since the p-value (0.0400) is less than the significance level (0.05), you would reject the null hypothesis, indicating that there is a statistically significant difference in the average number of trades per year compared to the previous year.

**Answer:** 0.0400
The p-value for the test is 0.0400.

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