A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-1:00pm lunch period. The waiting time of all customers during this hour is recorded over the period of a week. A random sample of 30 customers is selected and their waiting time is recorded (see data file Bank 1). At the 0.05 level of significance is there evidence that the population mean waiting time is less than 5 minutes?

Question

A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-1:00pm lunch period. The waiting time of all customers during this hour is recorded over the period of a week. A random sample of 30 customers is selected and their waiting time is recorded (see data file Bank 1). At the 0.05 level of significance is there evidence that the population mean waiting time is less than 5 minutes?

Answer 1

We can’t see “data file Bank 1”. Can’t copy and paste here.

Answer 2

To determine if there is evidence that the population mean waiting time is less than 5 minutes, we can conduct a hypothesis test.

Here's how we can approach it:

Step 1: State the null hypothesis (H0) and the alternative hypothesis (H1)

H0: The population mean waiting time is equal to 5 minutes.
H1: The population mean waiting time is less than 5 minutes.

Step 2: Set the significance level (α)

The significance level (α) is given in the problem as 0.05. This signifies that we want to be 95% confident in our results.

Step 3: Select the appropriate statistical test

In this case, since we have the sample mean and sample size, and we want to compare it to a known population mean, we can use a one-sample t-test.

Step 4: Calculate the test statistic

For a one-sample t-test, the test statistic is calculated using the formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Step 5: Determine the critical value

The critical value is based on the significance level and the degrees of freedom. Since we have 30 sample observations, the degrees of freedom is 30 - 1 = 29. Using a t-distribution table, we can find the critical value for a one-tailed test with a significance level of 0.05 and 29 degrees of freedom.

Step 6: Compare the test statistic with the critical value

If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 7: Interpret the results

Based on the outcome of the hypothesis test, we can draw a conclusion about the evidence for the population mean waiting time being less than 5 minutes.

I hope this was helpful! Let me know if you have any further questions.