Question

Directions: Answer each question to the best of your ability. Please show all work (including the 7 steps of
Hypothesis Test) and round decimals to the nearest ten-thousandths.

3. A student organization uses the proceeds from a particular soft-drink dispensing machine to finance its
activities. The price per can had been $0.50 for a long time, and the average daily revenue during that
period had been $51.50. The price was recently increased to $0.60 per can. A random sample of 20 days
after the price increase yielded a sample average revenue and sample standard deviation of $47.30 and
$4.20, respectively. Does this information suggest that the true average daily revenue has decreased
from its value before the price increase? Test the appropriate hypothesis using ? = 0.10.

Answer 1

Step 1: State the Null Hypothesis.

H0: True average daily revenue after the price increase = $51.50

Step 2: State the Alternative Hypothesis.

H1: True average daily revenue after the price increase < $51.50

Step 3: Set the significance level.

The significance level ? = 0.10.

Step 4: Collect Data

Sample mean, = $47.30

Sample standard deviation, s = $4.20

Standard error of mean = s / = 4.20 / = 0.9391486

Step 5: Calculate a test statistic

Test statistic = ( - ) / Std error = (47.30 - 51.50) / 0.9391486 = -4.47

Step 6: Calculate p-value and Decision

Since we do not the population standard deviation, we will use t distribution for the hypothesis test.

Degree of freedom = n - 1 = 20 - 1 = 19

P-value = P(t < -4.47, df = 19) = 0.0001

Since p-value is less than 0.10 significance level, we reject null hypothesis H0.

Step 7: Conclusion about H₀

We conclude that there is significant evidence that true average daily revenue after the price increase is less than $51.50 and has decreased.