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 after the price increase
yielded a sample mean daily revenue and sample standard deviation of $70.00 and $4.25, respectively.
Does this information suggest that the mean daily revenue has decreased from its value before the price
increase? Test the appropriate hypotheses using alpha = 0.05
a) State the appropriate null and alternative hypotheses
b) Find the test statistics
c) Use technology to find the P-value
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a) The appropriate null and alternative hypotheses are:
Null hypothesis (H0): The mean daily revenue is equal to its value before the price increase (μ = $75.00)
Alternative hypothesis (Ha): The mean daily revenue has decreased from its value before the price increase (μ < $75.00)
b) The test statistic can be found using the formula:
t = (x̄ - μ) / (s / √n)
Where:
x̄ = sample mean daily revenue ($70.00)
μ = population mean daily revenue before the price increase ($75.00)
s = sample standard deviation ($4.25)
n = sample size
Plugging in the values:
t = (70 - 75) / (4.25 / √n)
t = -5 / (4.25 / √n)
c) To find the p-value using technology, we need the test statistic and the degrees of freedom. The degrees of freedom can be calculated using the formula:
df = n - 1
Once we have both the test statistic and degrees of freedom, we can use a t-distribution table or a calculator to find the p-value.
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