Question

A student organization uses the proceeds from a soft drink vending machine to finance its activities. The price per can was $0.75 for a long time, and the mean daily revenue during that period was $75.00. The price was recently increased to $1.00 per can. A random sample of

n = 24 days
after the price increase yielded a sample mean daily revenue and sample standard deviation of $70.00 and $4.20, respectively. Does this information suggest that the mean daily revenue has decreased from its value before the price increase? Test the appropriate hypotheses using
= 0.05.Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

Answer 1

Since the P-value (0.249) is greater than the significance level (α = 0.05), we fail to reject the null hypothesis. There is not enough evidence at the 5% significance level to conclude that the mean daily revenue has decreased after the price increase.

How can you know whether the information suggests that the mean daily revenue has decreased from its value before the price increase?

Null Hypothesis (H 0): The mean daily revenue has not decreased after the price increase, i.e., µ after ≥ µ before = $75.00.

Alternative Hypothesis (H a): The mean daily revenue has decreased after the price increase, i.e., µ after < µ before = $75.00.

Test Statistic:

We will use a one-sample t-test since we don't know the population standard deviation and have a small sample size (n < 30). The test statistic is calculated as:

t = (x - µ 0) / (s / √n)

t = (70.00 - 75.00) / (4.20 / √24) ≈ -1.19

Under the null hypothesis, the t-statistic follows a t-distribution with n-1 degrees of freedom (df = 23). We need to find the two-tailed P-value associated with t = -1.19 and df = 23.

Using a t-distribution table, we find the P-value ≈ 0.249. Alternatively, some statistical software tools can directly calculate the P-value.

Since the P-value (0.249) is greater than the significance level (α = 0.05), we fail to reject the null hypothesis. There is not enough evidence at the 5% significance level to conclude that the mean daily revenue has decreased after the price increase.