Question

The number of concurrent users for some internet service provider has always averaged 8000 with a standard deviation of σ =900. After an equipment upgrade, the average number of users at 49 randomly selected moments of time is 8100. Assume that the standard deviation of the number of concurrent users has not changed after the upgrade

Using hypothesis testing, determine if this sample provides a significant evidence, at a 10% level of significance, that the mean number of concurrent users has increased
Make sure that you state the following in your work.
• Null null hypothesis,
• Alternative hypothesis,
• Test statistic
• Acceptance
• Conclusion (Based on the test statistic obtained from the sample, do we accept or reject the null hypothesis at a 10% level of significancel And why?)

Answer 1

Perform a hypothesis test to determine if the mean number of concurrent users has increased. The null hypothesis is that the mean has not increased (μ = 8000), and the alternative hypothesis is that it has increased (μ > 8000). Compare the z-value test statistic to the critical value at a 10% significance level to conclude.

Step-by-step explanation:

To assess whether the mean number of concurrent users for an internet service provider has significantly increased after an equipment upgrade, we need to perform a hypothesis test. The null hypothesis (H0) is that the mean number of users has not increased, implying μ = 8000. The alternative hypothesis (Ha) is that the mean number has increased, so μ > 8000.

To calculate the test statistic, we use the formula: z = (x - μ) / (σ / √n), where x is the sample mean (8100), μ is the population mean (8000), σ is the standard deviation (900), and n is the sample size (49). Plugging in the values gives us a z-value.

At a 10% level of significance, the z-value should be compared with the critical value from the Z-table that corresponds to a 90% confidence level (z-critical value). If the calculated z-value is greater than the z-critical value, we reject the null hypothesis. Otherwise, we do not reject it.

In conclusion, if our calculated test statistic z is greater than the z-critical value, we have significant evidence at a 10% significance level to suggest that the mean number of users has increased post-upgrade. Otherwise, we do not have sufficient evidence to support the claim that the mean has increased, and therefore would not reject the null hypothesis.