A firm hires a pool of financial consultants to discuss portfolio recommendations with its clients. The CEO believes that another financial consultant should be hired if the average phone consultation exceeds 350 seconds. A random sample of 100 phone calls revealed a mean of 375 seconds. The population standard deviation is 150 seconds. Should another financial consultant be hired? Use a 5% significance level.
I got 1.66667 so we should hire a new consultant?
Yes. See your other post for more detail.
To determine whether another financial consultant should be hired, we will conduct a hypothesis test using the given information.
Step 1: State the hypotheses:
- Null hypothesis (H0): The average phone consultation time is not greater than 350 seconds. (μ <= 350)
- Alternative hypothesis (Ha): The average phone consultation time is greater than 350 seconds. (μ > 350)
Step 2: Set the significance level:
The given significance level is 5%, which means α = 0.05.
Step 3: Compute the test statistic:
We will use the z-test since we know the population standard deviation and the sample size is greater than 30.
The formula for the z-test is:
z = (x̄ - μ) / (σ / √n)
Where:
x̄ is the sample mean (375 seconds)
μ is the population mean (350 seconds)
σ is the population standard deviation (150 seconds)
n is the sample size (100)
Substituting the values:
z = (375 - 350) / (150 / √100)
z = 25 / (150 / 10)
z = 25 / 15
z = 1.667
Step 4: Determine the critical value:
Since the alternative hypothesis is one-sided (greater than), we need to find the critical value from the right-tail of the z-distribution.
Using a z-table or calculator, we can find that the critical value for a 5% significance level (α = 0.05) is approximately 1.645.
Step 5: Make a decision:
If the test statistic (z) is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
In this case, z = 1.667 is greater than the critical value of 1.645.
Step 6: Draw a conclusion:
Since the test statistic (z) is greater than the critical value, we reject the null hypothesis (H0). This means there is enough evidence to conclude that the average phone consultation time exceeds 350 seconds.
Therefore, based on the given significance level of 5%, the firm should hire another financial consultant.